Inclusion Criteria:

          -  Groups 1 and 2 only: Biopsy-proven participants with relapsed or refractory NHL of
             DLBCL, FL or MZL..

          -  Groups 3, and 4 only: Biopsy-proven participants with relapsed or refractory DLBCL..

          -  Groups 5 only: Biopsy-proven participants with relapsed or refractory DLBCL..

          -  Participants must have at least 1 bi-dimensionally measurable lesion.

          -  -ECOG performance status of 0 to 2.

          -  Participants with protocol defined laboratory criteria at screening

          -  Groups 1 and 2 only:

        Received at least 1 previous systemic therapy line for the treatment of NHL. At least 1
        previous therapy line must have included a CD20-targeted therapy (eg, RTX).

        -Groups 3, 4a, and 4b only: Received at least 1, but no more than 3, previous systemic
        therapy lines for the treatment of DLBCL. At least 1 previous therapy line must have
        included a CD20-targeted therapy (eg, RTX).

        - Group 5 only: Participant must have: a. Untreated DLBCL. b. Ann Arbor Stage III to IV. c.
        IPI status of 3 to 5 or age-adjusted IPI 2-3 (in Group 5 only). d. Appropriate candidate
        for R-CHOP. e. LVEF of ≥ 50%, assessed by echocardiography.

        -Willingness to avoid pregnancy or fathering children.

        -In the opinion of investigator, the participant must: a. Not have a history of
        noncompliance in relation to medical regimens or be considered potentially unreliable
        and/or uncooperative.

        b. Be able to understand the reason for complying with the special conditions of the
        pregnancy prevention risk management plan and give written acknowledgement of this.

        Exclusion Criteria:

        -Any other histological type of lymphoma

          -  History of prior non-hematologic malignancy

          -  Congestive heart failure requiring use of ongoing maintenance therapy for
             life-threatening ventricular arrhythmias.

          -  Participants with known positive test result for hepatitis C, and hepatitis B.

          -  Known seropositive for or history of active viral infection with HIV.

          -  Known active bacterial, viral, fungal, mycobacterial, or other infection at screening.

          -  Known CNS lymphoma involvement - present or past medical history.

          -  History or evidence of clinically significant cardiovascular, CNS and/or other
             systemic disease that would in the investigator's opinion preclude participation in
             the study or compromise the participant's ability to give informed consent.

          -  History or evidence of rare hereditary problems of galactose intolerance, Lapp lactase
             deficiency or glucose-galactose malabsorption.

          -  History or evidence of interstitial lung disease.

          -  Vaccination with live vaccine within 21 days prior to study treatment (Note:
             throughout the study treatment period and at least 6 months after end of treatment,
             vaccination with live vaccines should be avoided).

          -  Major surgery within up to 30 days prior to signing the ICF, unless the participant is
             recovered at the time of signing the ICF.

          -  Any anticancer and/or investigational therapy within 14 days prior to the start of
             Cycle 1

          -  Gastrointestinal abnormalities including the inability to take oral study treatment,
             requiring IV alimentation, or prior surgical procedure affecting absorption.

          -  Pregnancy or lactation.

          -  Groups 3 and 5 only: Participants who have history of deep venous thrombosis/embolism,
             threatening thromboembolism, stroke or known thrombophilia or are at a high risk for a
             thromboembolic event in the opinion of the investigator and who are not willing/able
             to take venous thromboembolic event prophylaxis during the entire treatment period if
             required

          -  Groups 4a and 4b only: Use or expected use during the study of any restricted
             medications, including potent CYP3A4 inhibitors or inducers within 14 days or 5
             half-lives (whichever is longer) before the date of study treatment administration

          -  Groups 1, 2, 3, 4a, and 4b only: Participants who have: a. Not discontinued
             CD20-targeted therapy, chemotherapy, radiotherapy, investigational anticancer therapy,
             or other lymphoma-specific therapy within the 14 days prior to Day 1 dosing.

             b. In the opinion of the investigator, not recovered sufficiently from the adverse
             toxic effects of prior therapies.

             c. Previous treatment with CD19-targeted therapy (eg, CD19-CAR-T therapies, other CD19
             mAbs including bispecific and ADCs).

             d. Group 3 only: Been previously treated with IMiDs (eg, thalidomide or LEN). e. Group
             4a and 4b only: Been previously treated with selective PI3Kδ or pan-PI3K inhibitors
             (eg, idelalisib, copanlisib, duvelisib) and/or Bruton's tyrosine kinase inhibitors
             (eg, ibrutinib).

             f. A history of hypersensitivity to compounds of similar biological or chemical
             composition to tafasitamab, IMiDs, and/or the excipients contained in the study
             treatment formulations (citric acid monohydrate, polysorbate 20, sodium citrate
             dehydrate and trehalose dihydrate).

             g. Undergone ASCT within the period ≤ 3 months before the signing of the ICF.
             Participants who have a more distant history of ASCT must exhibit full hematological
             recovery before enrolment into the study.

             h. Undergone previous allogenic stem cell transplantation. i. Concurrent treatment
             other anticancer or experimental treatments.

          -  Group 5 only: Participants who have: a. A history of radiation therapy to ≥ 25% of the
             bone marrow for other diseases or history of anthracycline therapy.

             b. A history of hypersensitivity or contraindication to any component of R-CHOP, LEN,
             or compounds of similar biological or chemical composition as tafasitamab and/or the
             excipients contained in the study treatment formulations or R-CHOP.

             c. Contraindication to any of the individual components of R-CHOP. d. Any anticancer
             and/or investigational therapy within 30 days prior to the start of Cycle 1, except
             for permitted prephase treatment defined below.