Inclusion Criteria:

          -  Written informed consent and HIPAA authorization for release of personal health
             information prior to registration. NOTE: HIPAA authorization may be included in the
             informed consent or obtained separately.

          -  Age ≥ 18 years at the time of consent.

          -  Histologically or cytologically confirmed non-squamous, non-small cell lung cancer

          -  Locally advanced or metastatic disease, not amenable to curative surgery or
             radiotherapy.

          -  Patients must have one of the following:

               -  NSCLC which harbors Epidermal Growth Factor Receptor (EGFR) Exon 19 deletion.

               -  NSCLC which harbors EGFR L858R mutation. EGFR deletion/mutation must be
                  documented by a Clinical Laboratory Improvement Amendments (CLIA) certified test
                  (either from tissue or ctDNA from blood is allowed). If EGFR deletion/mutation
                  testing has not been done, it should be ordered per standard of care.

          -  Eastern Cooperative Oncology Group (ECOG) performance status 0-1 (Appendix A)

          -  Measurable disease per RECIST 1.1

          -  Patients with brain metastases are eligible if they are asymptomatic, are treated, or
             are neurologically stable for at least two weeks without the use of steroids or on
             stable or decreasing dose of ≤ 10 mg daily prednisone (or equivalent). These criteria
             must be met on day of consent.

          -  Ability to take pills by mouth

          -  Previous treatment with cytotoxic chemotherapy or immunotherapy is allowed

          -  Patients must have adequate hematologic, coagulation, hepatic, and renal function. All
             laboratory tests must be obtained less than 4 weeks from study entry. This includes:

               -  Absolute Neutrophil Count (ANC) >/= 1,500/mm3

               -  platelet count >/=100,000/mm3

               -  Hemoglobin (HgB) ≥ 9 g/dL (may be with transfusion)

               -  Creatinine ≤ 1.5x ULN or creatinine clearance (measured via 24-hour urine
                  collection) ≥40 mL/minute (that is, if serum creatinine is >1.5 times the ULN, a
                  24-hour urine collection to calculate creatinine clearance must be performed).

               -  The patient's urinary protein is ≤ 1+ on dipstick or routine urinalysis (UA); if
                  urine dipstick or routine analysis is ≥ 2+, a 24-hour urine collection for
                  protein must demonstrate < 1000 mg of protein in 24 hours to allow participation
                  in this protocol).

               -  International Normalized Ratio (INR) ≤ 1.5 and a partial thromboplastin time
                  (PTT) ≤ 5 seconds above the ULN (unless receiving anticoagulation therapy).
                  Patients receiving warfarin must be switched to low molecular weight heparin and
                  have achieved stable coagulation profile prior to first dose of protocol therapy.

               -  Total Serum Bilirubin ≤ 1.5 x ULN (Patients with known Gilbert Syndrome, a total
                  bilirubin ≤ 3.0 x ULN, with direct bilirubin ≤ 1.5 x ULN)

               -  Serum Glutamic Oxaloacetic Transaminase (SGOT), Serum Glutamic-Pyruvic
                  Transaminase (SGPT) ≤ 3 X ULN if no liver metastasis present

               -  SGOT, SGPT ≤ 5 X ULN if liver metastasis present

          -  Females of childbearing potential must not be breast feeding and must have a negative
             serum pregnancy test within 7 days of starting of treatment. The patient must agree to
             use adequate contraception for a minimum of two weeks prior to receiving study
             medication until 3 months after discontinuation of the study medication. Acceptable
             methods of contraception are listed in Section 5.5. NOTE: Women will be considered
             post-menopausal if they have been amenorrheic for the past 12 months without an
             alternative medical cause. The following age-specific requirements must also apply:
             Women < 50 years old: they would be considered post-menopausal if they have been
             amenorrheic for the past 12 months or more following cessation of exogenous hormonal
             treatments. The levels of Luteinizing Hormone (LH) and Follicle-Stimulating Hormone
             (FSH) must also be in the post-menopausal range (as per the institution). Women ≥ 50
             years old: they would be considered post-menopausal if they have been amenorrheic for
             the past 12 months or more following cessation of all exogenous hormonal treatments,
             or have had radiation-induced oophorectomy with the last menses > 1 year ago, or have
             had chemotherapy-induced menopause with >1 year interval since last menses, or have
             had surgical sterilization by either bilateral oophorectomy or hysterectomy.

          -  Non-sterilized males who are sexually active with a female partner of childbearing
             potential must use adequate contraception for the duration of the study and 4 months
             after the last dose of study medication. If male patients wish to father children they
             should be advised to arrange for freezing of sperm samples prior to the start of the
             study medication.

        Exclusion Criteria:

          -  Subjects unable to stop use of medications that are potent inducers of CYP3A4 or known
             to prolong QT interval. See Appendix B for additional details.

          -  Any prior history of other cancer within the prior 2 years with the exception of:
             adequately treated basal cell carcinoma, cervical intraepithelial neoplasia
             [CIN]/cervical carcinoma in situ, melanoma in situ or ductal carcinoma in situ [DCIS],
             localized Gleason 6 prostate cancer, papillary thyroid cancer or other non-melanoma
             skin cancers.

          -  Previous treatment with any EGFR TKIs, including erlotinib, gefitinib, afatinib,
             avitinib, dacomitinib, rociletinib, or osimertinib.

          -  Previous treatment with any anti-Vascular Endothelial Growth Factor (VEGF)
             medications, including vandetinib, nintedanib, bevacizumab, or ramucirumab.

          -  Spinal cord compression unless asymptomatic or stable for at least 2 weeks prior to
             start of study treatment.

          -  Any unresolved toxicities from prior therapy greater than CTCAE grade 1 (with the
             exception of alopecia grade 2) at the time of starting study treatment.

          -  Any evidence of severe or uncontrolled systemic diseases, including uncontrolled
             hypertension and active bleeding diatheses, which in the investigator's opinion makes
             it undesirable for the subject to participate in the trial or which would jeopardize
             compliance with the protocol, or active infection including hepatitis B, hepatitis C
             and human immunodeficiency virus (HIV). Screening for chronic conditions is not
             required.

          -  Refractory nausea and vomiting, chronic gastrointestinal diseases, inability to
             swallow the formulated product or previous significant bowel resection that would
             preclude adequate absorption of osimertinib.

          -  Past medical history of interstitial lung disease (ILD), drug-induced ILD, radiation
             pneumonitis which required steroid treatment, or any evidence of clinically active
             interstitial lung disease.

          -  Patients with uncharacterized eye disorders.

          -  Males and females of reproductive potential who are not using and effective method of
             birth control and females who are pregnant or breastfeeding or have a positive (urine
             or serum) pregnancy test prior to study entry.

          -  History of hypersensitivity of osimertinib or ramucirumab (or active or inactive
             excipients of osimertinib or ramucirumab)

          -  Judgment by the investigator that the patient should not participate in the study if
             the patient is unlikely to comply with study procedures, restrictions and requirement.

          -  Any of the following cardiac criteria:

               -  Mean resting corrected QT interval (QTc using Fridericia's formula) > 470 msec

               -  Any clinically important abnormalities in rhythm, conduction or morphology of
                  resting ECG e.g., complete left bundle branch block, third degree heart block,
                  second degree heart block, PR interval >250msec

               -  Any factors that increase the risk of QTc prolongation or risk of arrhythmic
                  events such as heart failure, hypokalemia, congenital long QT syndrome, family
                  history of long QT syndrome or unexplained sudden death under 40 years of age in
                  first degree relatives or any concomitant medication known to prolong the QT
                  interval.

               -  The patient has experienced any arterial thromboembolic events, including but not
                  limited to myocardial infarction, transient ischemic attack, cerebrovascular
                  accident, or unstable angina, within 6 months prior to first dose of protocol
                  therapy.

               -  The patient has uncontrolled or poorly-controlled hypertension (>160 mmHg
                  systolic or > 100 mmHg diastolic for >4 weeks) despite standard medical
                  management.

          -  The patient has experienced any Grade 3-4 GI bleeding within 3 months prior to first
             dose of protocol therapy.

          -  The patient has a history of deep vein thrombosis (DVT), pulmonary embolism (PE), or
             any other significant thromboembolism (venous port or catheter thrombosis or
             superficial venous thrombosis are not considered "significant") during the 3 months
             prior to first dose of protocol therapy.

          -  The patient has cirrhosis at a level of Child-Pugh B (or worse) or cirrhosis (any
             degree) and a history of hepatic encephalopathy or clinically meaningful ascites
             resulting from cirrhosis. Clinically meaningful ascites is defined as ascites from
             cirrhosis requiring diuretics or paracentesis.

          -  Any hemoptysis (defined as bright red blood or ≥ 1/2 teaspoon) within 2 months prior
             to first dose of protocol therapy or with radiographic evidence of intratumor
             cavitation or has radiologically documented evidence of major blood vessel invasion or
             encasement by cancer.

          -  The patient has a prior history of GI perforation/fistula (within 6 months of first
             dose of protocol therapy) or risk factors for perforation.

          -  The patient has a serious or nonhealing wound, ulcer, or bone fracture within 28 days
             prior to first dose of protocol therapy.

          -  The patient has undergone major surgery within 28 days prior to first dose of protocol
             therapy, or minor surgery/subcutaneous venous access device placement within 7 days
             prior to the first dose of protocol therapy. The patient has elective or planned major
             surgery to be performed during the course of the clinical trial.

          -  The patient is receiving chronic antiplatelet therapy, including aspirin, nonsteroidal
             anti-inflammatory drugs (NSAIDs, including ibuprofen, naproxen, and others),
             dipyridamole or clopidogrel, or similar agents. Once-daily aspirin use (maximum dose
             325 mg/day) is permitted.