Inclusion Criteria:

          -  Histologic documentation of disease: B-cell NHL or CLL requiring therapy; All
             participants must have relapsed or refractory disease with no other approved therapies
             available that would be more appropriate in the investigator's judgment.

        B cell NHL: In addition, the following disease-specific criteria outlined below must be met
        a) If diffuse large B-cell lymphoma (DLBCL): received, or not eligible for high-dose
        chemotherapy and autologous stem cell transplantation with curative intent, b) If
        follicular lymphoma (FL)/ marginal zone lymphoma (MZL) (except mucosa-associated lymphoid
        tissue [MALT]), or Waldenstrom macroglobulinemia (WM): previously treated with at least 1
        prior line of systemic therapy containing an anti-CD20 antibody, c) If mantle cell lymphoma
        (MCL): previously treated with at least 1 prior line of systemic therapy containing an
        anti-CD20 antibody. CLL or small lymphocytic lymphoma (SLL): relapsed or refractory with at
        least 1 prior line of systemic therapy containing a bruton tyrosine kinase inhibitor (BTKi)
        and for Part B: participants must have measurable disease as defined by the appropriate
        disease response criteria

          -  Eastern Cooperative Oncology Group (ECOG) performance status Grade of 0 or 1

          -  Cardiac parameters within the following range: corrected QT interval (QTc intervals
             corrected using Fridericia's formula [QTcF]) less than or equal to (<=) 480
             milliseconds (ms) based on the average of triplicate assessments performed no more
             than 5 (plus minus [+ -] 3) minutes apart

          -  Women of childbearing potential must have a negative highly sensitive serum pregnancy
             test (Beta human chorionic gonadotropin) at screening and prior to the first dose of
             study drug

          -  Women must be: a) not of childbearing potential, b) of childbearing potential and
             practicing a highly effective, preferably user independent method of contraception
             (failure rate of less than (<) 1 percent (%) per year when used consistently and
             correctly) and agrees to remain on a highly effective method while receiving study
             drug and until 90 days after last dose

        Exclusion Criteria:

          -  Known active central nervous system (CNS) involvement with lymphoma

          -  Prior solid-organ transplantation

          -  Either of the following: a) received an autologous stem cell transplant <=3 months
             before the first dose of JNJ 75348780, b) prior treatment with allogenic stem cell
             transplant <= 6 months before the first dose of JNJ-75348780, or has evidence of graft
             versus host disease that requires immunosuppressant therapy

          -  Prior chemotherapy, targeted therapy, immunotherapy or radiotherapy (with the
             exclusion of palliative radiation to limited sites that do not interfere with response
             assessment based on a sufficient number of other sites), within 2 weeks before the
             first administration of study drug. For investigational agents where the half-life is
             known, there should be a treatment-free window of at least 2 weeks or 5 half-lives,
             whichever is longer. For investigational agents with long half-lives a wash-out of 4
             weeks is acceptable

          -  Active autoimmune disease that requires systemic immunosuppressive medications
             (example, chronic corticosteroid, methotrexate, or tacrolimus)