Inclusion Criteria:

          1. Provision of signed informed consent.

          2. Male and non-pregnant females who are aged 18 years or older at the time of provision
             of informed consent.

          3. Histopathologically or cytologically documented Stage IV adenocarcinoma non-small cell
             lung cancer (NSCLC). Note: Patients with a mixed histology including a significant
             area of adenocarcinoma histology are eligible.

          4. Cohort A only: Has disease progression on or after a prior platinum-containing
             chemotherapy. Note: Patients with Epidermal growth factor receptor (EGFR) mutations or
             ALK genomic rearrangements must have documented disease progression on at least one
             licensed therapy for these indications and may not have received platinum-containing
             chemotherapy.

          5. Cohort B only:

               1. Has received a maximum of two prior lines of therapy in the advanced setting,
                  with the most recent treatment regimen containing an anti-PD-(L)1-therapy (as
                  monotherapy or in combination).

               2. Must have had disease control (SD, PR or CR) for at least 6 months on most recent
                  treatment containing at least 2 doses of anti-PD-(L)1-therapy.

               3. Has disease progression when entering screening and this must be within 12 weeks
                  of last dose of most recent treatment containing an anti-PD-(L)1 therapy.
                  Progression should have been confirmed in one of the following ways: (i) Having
                  had two scan assessments completed at least 4 weeks apart, both showing
                  progression according to RECIST 1.1 or (ii) having had one scan assessment
                  completed showing disease progression according to standards used for previous
                  therapy combined with rapid disease progression / clinical progression.

          6. Measurable disease as defined by RECIST 1.1 on computed tomography (CT) or magnetic
             resonance imaging (MRI) and as determined by the site study team. Tumor lesions
             situated in a previously irradiated area are considered measurable if progression has
             been demonstrated in such lesions.

          7. Provision of suitable tumor tissue for the analysis of Axl kinase expression and PD-L1
             expression. Suitable tumor tissue must consist of a minimum of newly acquired (fresh)
             tumor tissue sample (as a FFPE block), together with either further newly acquired
             tumor tissue (i.e. further FFPE block) or an archival tumor tissue sample (as a
             further FFPE block or further 10 unstained slides). See Section 5.3.13 for further
             details.

          8. Eastern Cooperative Oncology Group (ECOG) performance score 0 or 1.

          9. Life expectancy of at least 3 months.

         10. Adequate organ function confirmed at Screening within 10 days of treatment initiation
             - as evidenced by:

               1. Platelet count ≥100,000 /mm3;

               2. Hemoglobin ≥9.0 g/dL (≥5.6 mmol/L);

               3. Absolute neutrophil count (ANC) >1,500 /mm3;

               4. Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤2.5 times
                  the upper limit of normal (ULN), or ≤5 times the ULN for patients with liver
                  metastases;

               5. Total bilirubin ≤1.5 times the ULN.

               6. Creatinine ≤1.5 times the ULN or calculated creatinine clearance 60 mL/min (by
                  Cockcroft Gault formula);

               7. International Normalized Ratio (INR) or Prothrombin Time (PT) ≤1.5 times the ULN
                  and Activated Partial Thromboplastin Time (aPTT) ≤1.5 times the ULN. Note: If
                  patient is receiving anticoagulant therapy, then PT or Partial thromboplastin
                  time (PTT) must be within therapeutic range of intended use of anticoagulants;

         11. Female patients of childbearing potential must have a negative urine or serum
             pregnancy test within 72 hours prior to the first dose of study treatment. If urine
             test is positive or cannot be confirmed as negative, a serum pregnancy test will be
             required.

         12. Patients (both male and female) of reproductive potential must be willing to practice
             highly effective methods of contraception throughout the study and for 120 days after
             the last dose of study medication. Abstinence is acceptable if this is the usual
             lifestyle for the patient. Female patients are considered NOT of childbearing
             potential if they have a history of surgical sterility or evidence of post-menopausal
             status defined as any of the following:

               1. ≥45 years of age and has not had menses for more than 1 year;

               2. Amenorrheic for >2 years without a hysterectomy and oophorectomy and a follicle
                  stimulating hormone (FSH) value in the postmenopausal range upon Screening
                  evaluation;

               3. Post hysterectomy, oophorectomy or tubal ligation. Documented hysterectomy or
                  oophorectomy must be confirmed with medical records of the actual procedure or
                  confirmed by an ultrasound. Tubal ligation must be confirmed with medical records
                  of the actual procedure.

         13. Have resolution of toxic effect(s) of the most recent prior chemotherapy to Grade 1 or
             less (except alopecia). If the patient received major surgery or radiation therapy of
             > 30 Gy, they must have recovered from the toxicity and/or complications from the
             intervention.

        Exclusion Criteria:

          1. Has disease suitable for local therapy administered with curative intent.

          2. Has received more than 1 prior line of chemotherapy for advanced or metastatic
             adenocarcinoma of the lung. Cohort B: Has received more than two prior lines of
             therapy for advanced or metastatic adenocarcinoma of the lung. Note: Patients may have
             received additional prior radiotherapy or chemotherapy in the adjuvant setting,
             providing it was completed at least 6 months prior to start of study treatment.

          3. Cohort A only: Has received prior therapy with an immunomodulatory agent.

          4. Has a known additional malignancy that is progressing or requires active treatment.
             Note: Exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of
             the skin that has undergone potentially curative therapy or in situ cervical cancer.

          5. Has known active central nervous system (CNS) metastases and/or carcinomatous
             meningitis. Note: Patients with previously treated brain metastases may participate
             provided they are stable (without evidence of progression by imaging (using the
             identical modality for each assessment, either MRI or CT scan) for at least 4 weeks
             prior to the first dose of trial treatment and any neurological symptoms have returned
             to baseline), have no evidence of new or enlarging brain metastases, and are not using
             steroids for at least 7 days prior to trial treatment.

          6. History of the following cardiac conditions:

               1. Congestive cardiac failure of >Grade II severity according to the NYHA (Appendix
                  C: defined as symptomatic at less than ordinary levels of activity).

               2. Ischemic cardiac event including myocardial infarction within 3 months prior to
                  first dose.

               3. Uncontrolled cardiac disease, including unstable angina, uncontrolled
                  hypertension (i.e. sustained systolic BP >160 mmHg or diastolic BP >90 mmHg), or
                  need to change medication due to lack of disease control within 6 weeks prior to
                  the provision of consent.

               4. History or presence of sustained bradycardia (≤55 BPM), left bundle branch block,
                  cardiac pacemaker or ventricular arrhythmia. Note: Patients with a
                  supraventricular arrhythmia requiring medical treatment, but with a normal
                  ventricular rate are eligible.

               5. Family history of long QTc syndrome; personal history of long QTc syndrome or
                  previous drug-induced QTc prolongation of at least Grade 3 (QTc >500ms).

          7. Abnormal left ventricular ejection fraction on echocardiography or MUGA (less than the
             lower limit of normal for a patient of that age at the treating institution or <45%,
             whichever is lower).

          8. Current treatment with any agent known to cause Torsades de Pointes which cannot be
             discontinued at least five half-lifes or two weeks prior to the first dose of study
             treatment.

          9. Screening 12-lead ECG with a measurable QTc interval according to Fridericia's
             correction >450 ms.

         10. Is currently participating and receiving study therapy or has participated in a study
             of an investigational agent and received study therapy or used an investigational
             device within 4 weeks of the first dose of study treatment.

         11. Received chemotherapy or targeted small molecule therapy or radiation therapy within 2
             weeks prior to starting study treatment or who has not recovered (i.e. ≤Grade 1 at
             baseline) from AEs due to a previously administered agent. Note: Patients with ≤Grade
             2 alopecia are an exception to this criterion. If the patient received major surgery,
             they must have recovered adequately from the toxicity and/or complications from the
             intervention prior to starting therapy.

         12. Received an anti-cancer monoclonal antibody (mAb) within 4 weeks prior to the first
             dose of study treatment or who has not recovered (i.e. ≤Grade 1 or baseline) from AEs
             due to agents administered more than 4 weeks earlier.

         13. Major surgery within 28 days prior to start of study treatment and failure to have
             recovered adequately from the toxicity and/or complications from the intervention
             prior to the first dose of study treatment. Note: Major surgery does not include
             procedures for insertion of venous catheters or biopsies.

         14. Received transfusion of blood products (including platelets or red blood cells) or
             administration of colony stimulating factors (including G-CSF, GM-CSF or recombinant
             erythropoetin) within 4 weeks prior to the first dose of study treatment. Note:
             Patients receiving stable dose of growth factors with a haemoglobin value that meets
             Inclusion Criterion 9b may be included.

         15. Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any
             other form of immunosuppressive therapy within 7 days prior to the first dose of study
             treatment.

         16. Active autoimmune disease that has required systemic treatment in past 2 years (i.e.
             with use of disease modifying agents, corticosteroids or immunosuppressive drugs).
             Note: Replacement therapy (e.g. thyroxine, insulin, or physiologic corticosteroid
             replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a
             form of systemic treatment.

         17. Known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies).

         18. Has known active infection with Hepatitis B (e.g., HBsAg reactive) or Hepatitis C
             (e.g., HCV Ribonucleic acid (RNA) [qualitative] is detected). Note: i) Patients with a
             history of hepatitis B infection are eligible provided they are hepatitis B surface
             antigen negative ii) Patients with a history of hepatitis C infection are eligible
             provided they have no evidence of hepatitis C RNA using a qPCR at least 6 months after
             completing treatment for hepatitis C infection.

         19. Has received a live-virus vaccination within 30 days of planned treatment start. Note:
             Seasonal flu vaccines that do not contain live virus are permitted.

         20. Has a history of (non-infectious) pneumonitis that required steroids or current
             pneumonitis.

         21. Has a history of interstitial lung disease.

         22. Inability to swallow or tolerate oral medication.

         23. Existing gastrointestinal disease affecting drug absorption such as celiac disease or
             Crohn's disease, or previous bowel resection which is considered to be clinically
             significant or could interfere with absorption.

         24. Known lactose intolerance.

         25. Requires vitamin K antagonists. Note: Patients receiving low doses prescribed to
             maintain the patency of venous access devices may be included. Note: Factor Xa
             antagonists are permitted.

         26. Treatment with any of the following: histamine receptor 2 inhibitors, proton pump
             inhibitors or antacids within 7 days of start of study treatment.

         27. Treatment with any medication which is predominantly metabolized by CYP3A4 and has a
             narrow therapeutic index.

         28. Known hypersensitivity to bemcentinib, pembrolizumab, or any of their excipients.

         29. Any evidence of severe or uncontrolled systemic conditions (e.g. severe hepatic
             impairment) or current unstable or uncompensated respiratory or cardiac conditions, or
             ongoing.

         30. Has active infection requiring systemic therapy (apart from cutaneous infections).

         31. Has received radiation to the lung of >30 Gy within 6 months of first dose.

         32. Has a history or current evidence of any condition, therapy, or laboratory abnormality
             that might confound the results of the trial, interfere with the patient's
             participation for the full duration of the trial, or means it is not in the best
             interest of the patient to participate, in the opinion of the Investigator

         33. Is pregnant or breastfeeding, or expecting to conceive or father children within the
             projected duration of the trial, starting from Screening through to 120 days after the
             last dose of study treatment.

         34. Has known psychiatric or substance abuse disorders that would interfere with
             cooperation with the requirements of the trial.

         35. Cohort B only: Has an EGFR mutation or ALK genomic rearrangement.