Inclusion Criteria:

          1. Male or female participant aged 18 years or older

          2. Pathologic diagnosis of DLBCL or MCL (For Italy Sites Only: MCL patients are
             excluded.)

          3. Participants with DLBCL must have relapsed or refractory disease and have failed or
             been intolerant to available standard therapy

          4. Participants with MCL must have relapsed or refractory disease and have received at
             least one prior line of therapy (For Italy Sites Only: This exclusion criterion is not
             applicable)

          5. Participants who have received previous CD19-directed therapy must have a biopsy which
             shows CD19 expression after completion of the CD19-directed therapy

          6. Measurable disease as defined by the 2014 Lugano Classification

          7. Availability of formalin-fixed paraffin-embedded (FFPE) tumor tissue block (or minimum
             10 freshly cut unstained slides if block is not available)

          8. ECOG performance status 0 to 2

          9. Screening laboratory values within the following parameters:

               1. Absolute neutrophil count (ANC) ≥1.0 × 103/µL (off growth factors at least 72
                  hours)

               2. Platelet count ≥75 × 103/µL without transfusion in the past 7 days

               3. Hemoglobin ≥8 g/dL (4.96 mmol/L), transfusion allowed

               4. Alanine aminotransferase (ALT), aspartate aminotransferase (AST), and gamma
                  glutamyl transferase (GGT) ≤2.5 × the ULN

               5. Total bilirubin ≤1.5 × ULN (participants with known Gilbert's syndrome may have a
                  total bilirubin up to ≤3 × ULN)

               6. Blood creatinine ≤1.5 × ULN or calculated creatinine clearance ≥60 mL/min by the
                  Cockcroft and Gault equation

         10. Negative beta-human chorionic gonadotropin (β-HCG) pregnancy test within 7 days prior
             to start of study drugs on C1D1 for women of childbearing potential

         11. Women of childbearing potential must agree to use a highly effective method of
             contraception from the time of giving informed consent until at least 9 months after
             the last dose of loncastuximab tesirine or 1 month after last dose of ibrutinib,
             whichever comes last. Men with female partners who are of childbearing potential must
             agree that they will use a highly effective method of contraception from the time of
             giving informed consent until at least 6 months after the participant receives his
             last dose of loncastuximab tesirine or 3 months after last dose of ibrutinib,
             whichever comes last

        Exclusion Criteria:

          1. Known history of hypersensitivity to or positive serum human anti-drug antibody (ADA)
             to a CD19 antibody

          2. Known history of hypersensitivity to ibrutinib

          3. Previous therapy with ibrutinib or other BTK inhibitors

          4. Previous therapy with loncastuximab tesirine

          5. Requires treatment or prophylaxis with a moderate or strong cytochrome P450 (CYP) 3A
             inhibitor

          6. Allogenic or autologous transplant within 60 days prior to start of study drugs (C1D1)

          7. Active graft-versus-host disease

          8. Post-transplantation lymphoproliferative disorder

          9. Active autoimmune disease, including motor neuropathy considered of autoimmune origin
             and other central nervous system (CNS) autoimmune disease

         10. Known seropositive and requiring anti-viral therapy for human immunodeficiency (HIV)
             virus, hepatitis B virus (HBV), or hepatitis C virus (HCV).

         11. History of Stevens-Johnson syndrome or toxic epidermal necrolysis

         12. Lymphoma with active CNS involvement at the time of screening, including
             leptomeningeal disease

         13. Clinically significant third space fluid accumulation (i.e., ascites requiring
             drainage or pleural effusion that is either requiring drainage or associated with
             shortness of breath)

         14. Breastfeeding or pregnant

         15. Significant medical comorbidities, including but not limited to, uncontrolled
             hypertension (blood pressure [BP] ≥160/100 millimeters of mercury (mmHg) repeatedly),
             unstable angina, congestive heart failure (greater than New York Heart Association
             class II), electrocardiographic evidence of acute ischemia, coronary angioplasty or
             myocardial infarction within 6 months prior to screening, uncontrolled atrial or
             ventricular cardiac arrhythmia, poorly controlled diabetes mellitus, or severe chronic
             pulmonary disease, or tuberculosis infection (tuberculosis screening based on local
             standards).

         16. Major surgery, radiotherapy, chemotherapy, or other anti-neoplastic therapy within 14
             days prior to start of study drugs (C1D1), except shorter if approved by the Sponsor

         17. Use of any other experimental medication within 14 days prior to start of study drugs
             (C1D1)

         18. Planned live vaccine administration after starting study drugs (C1D1)

         19. Any condition that could interfere with the absorption or metabolism of ibrutinib
             including malabsorption syndrome, disease significantly affecting gastrointestinal
             function, or resection of the stomach or small bowel

         20. Inherited or acquired bleeding disorders

         21. Ongoing anticoagulation treatment, except for low-dose heparinisation or equivalent

         22. Failure to recover to Grade ≤1 (Common Terminology Criteria for Adverse Events [CTCAE]
             version 4.0) from acute non-hematologic toxicity (Grade ≤2 neuropathy or alopecia) due
             to previous therapy prior to screening

         23. Congenital long QT syndrome or a corrected QTcF interval of >480 ms at screening
             (unless secondary to pacemaker or bundle branch block)

         24. Active second primary malignancy other than non-melanoma skin cancers, non metastatic
             prostate cancer, in situ cervical cancer, ductal or lobular carcinoma in situ of the
             breast, or other malignancy that the Sponsor's medical monitor and Investigator agree,
             and document should not be exclusionary

         25. Any other significant medical illness, abnormality, or condition that would, in the
             Investigator's judgement, make the participant inappropriate for study participation
             or put the participant at risk