Copanlisib in Combination With Venetoclax in Patients With Relapsed or Refractory B-cell Non-Hodgkin Lymphoma.

Inclusion Criteria: * Written informed consent according to Swiss law and ICH/GCP regulations before registration and prior to any trial specific procedures. * Histologically confirmed B-cell NHL lymphoma as per WHO classification for the escalation phase. FL or MZL for the expansion phase. * Patients with relapsed or refractory disease who have failed previous treatment (including chemotherapy plus anti CD20) for whom no effective standard treatment is available or refused by the patient. * Patients with a prior malignancy and treated with curative intention are eligible if all treatment of that malignancy was completed at least 2 years before registration and the patient has no evidence of disease at registration. Less than 2 years is acceptable for malignancies with low risk of recurrence and/or no late recurrence. * \> 1 two-dimensionally measurable nodal lesion in CT, PET/CT scan (preferable) or MRI, according to Cheson et al, 2014. * Tumor tissue (formalin fixed paraffin embedded (FFPE) slides/rolls) is available for the mandatory translational research. * Age ≥ 18 years. * WHO performance status 0-1 * Adequate bone marrow function: 1. Absolute neutrophil count (ANC) \>1.5 × 109/l (1 × 109/l if due to bone marrow involvement by lymphoma). Patient must not have received any hematologic growth factor within 14 days prior to registration. 2. Platelet count \>100 ×109/l (75 ×109/l if due to bone marrow involvement by lymphoma) * Adequate hepatic function: 1. total bilirubin ≤ 1.5 × ULN (except for patients with Gilbert's disease ≤ 3.0 × ULN), 2. AST and ALT ≤ 2.5 × ULN, or ≤ 5 × ULN under the assumption that abnormal values are tumor related. * Adequate renal function: estimated glomerular filtration rate (eGFR) ≥ 50 ml/min/1.73 m2 (according to CKD-EPI formula) * Adequate cardiac function: Left ventricular Ejection Fraction (LVEF) ≥ 50% as determined by echocardiography (ECHO). * Adequate coagulation function: INR ≤ 1.5 × ULN (the ULN for INR is defined with the value 1.2 for all sites, in case no ULN is documented in the lab certificates/sheets), aPTT ≤ 1.5 × ULN. * Women of childbearing potential (not surgically sterile or exceeding 2 years after the onset of menopause) must use highly effective contraception, are not pregnant or lactating and agree not to become pregnant during trial treatment and until 3 months after the last dose of investigational drug. A negative pregnancy test before inclusion into the trial is required for all women of childbearing potential. * Men agree not to donate sperm or to father a child during trial treatment and until 3 months after the last dose of investigational drug. * Patient is able and willing to swallow trial drug as whole tablet. Exclusion Criteria: * Patients with CLL/SLL. * Patients that require ramp-up of venetoclax, including MCL. Other histologies will be discussed with the coordinating investigator (CI). * Presence or history of CNS disease (either CNS lymphoma or lymphomatous meningeosis). Primary CNS disease. * Prior treatment with venetoclax, copanlisib or any other bcl-2 inhibitors or PIK3 inhibitors. * Prior allogeneic stem cell transplant (SCT), or autologous transplant less than 3 months prior to registration. * Concomitant or recent treatment with any other experimental drug (enrollment in another clinical trial. * Treatment with any anti-lymphoma therapies within 21 days prior to registration - except for local radiation therapy for palliative treatment of symptoms. * Not resolved grade ≥ 2 (per NCI CTCAE v5.0 toxicity (other than alopecia) from prior therapy at registration. * Severe or uncontrolled cardiovascular disease (congestive heart failure NYHA III or IV; (see Appendix 4), unstable or new onset angina pectoris, history of myocardial infarction within the last six months, serious arrhythmias requiring medication (with exception of atrial fibrillation or paroxysmal supraventricular tachycardia), significant QT-prolongation. * Uncontrolled hypertension (sustained systolic blood pressure \>150 mmHg and or diastolic \>90 mmHg) despite optimal medical management (per investigator's assessment). * Proteinuria of ≥ CTCAE grade 3 as assessed by a 24h total urine protein quantification or on a random urine sample, estimated by urine protein to creatinine ratio \> 3.5. * HbA1c \> 8.5%. * Lipase ≥ 1.5 x ULN. * History of cerebrovascular accident or intracranial hemorrhage within 6 months prior to registration. * Major surgery within 1 month prior to registration. * Known history of human immunodeficiency virus (HIV) or active chronic Hepatitis C or Hepatitis B Virus infection or any uncontrolled active systemic infection requiring intravenous (iv) antimicrobial treatment. All patients must be screened for HIV up to 28 days prior to study drug start using a blood test for HIV according to local regulations. All patients must be screened for hepatitis up to 28 days prior to study drug start using the routine hepatitis virus laboratory panel. Patients positive for hepatitis B surface antigen (HBsAg) or hepatitis B core antibody (HBcAb) will be eligible if they are negative for HBV-DNA, these patients should receive prophylactic antiviral therapy. Patients positive for anti-HCV antibody will be eligible if they are negative for HCV-RNA. * Active CMV infection. Patients who are CMV PCR positive at baseline will be excluded. * Malabsorption syndrome or other condition that precludes enteral route of administration. * Concomitant or prior use of immunosuppressive medication within 28 days before registration, with the exceptions of intranasal and inhaled corticosteroids, or systemic corticosteroids which must not exceed 10 mg/day of prednisone or a dose equivalent corticosteroid). * Has active autoimmune disease that has required systemic treatment in past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). 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. * Concomitant anticoagulation treatment with warfarin or equivalent vitamin K antagonists (e.g. phenprocoumon), factor Xa inhibitors (e.g. rivaroxaban, apixaban), direct thrombin inhibitors (e.g. dabigatran) or platelet inhibitors/antiplatelet agents. Exception: Aspirin (up to 300 mg/day) is allowed. * Concomitant treatment with strong CYP3A inducers or inhibitors (see http://medicine.iupui.edu/ and the FDA database of drug interactions. Concomitant treatment with moderate inhibitors or inducers during the DLT period. * Any concomitant drugs contraindicated for use with the trial drugs according to the approved product information. * Known hypersensitivity to trial drug(s) or to any component of the trial drug(s). * Any other serious underlying medical, psychiatric, psychological, familial or geographical condition, which in the judgment of the investigator may interfere with the planned staging, treatment and follow-up, affect patient compliance or place the patient at high risk from treatment-related complications.