Copanlisib and Combination Chemotherapy for the Treatment of Relapsed or Refractory Diffuse Large B-Cell Lymphoma or Relapsed Grade 3b Follicular Lymphoma

Subjects must meet one of the following criteria:

* Histologically confirmed relapsed/refractory DLBCL or grade 3b follicular lymphoma.

* Follicular lymphoma that has relapsed within 2 years of primary therapy that included an anti-CD20 antibody in combination with chemotherapy as measured from the date of the last dose of chemotherapy

Eastern Cooperative Oncology Group (ECOG) performance status =\< 2

Previous exposure to other PI3K inhibitors (except copanlisib) is acceptable provided there is no resistance (resistance defined as no response \[response defined as partial response (PR) or CR\] at any time during therapy), or progressive disease (PD) after any response (PR/CR) or after stable disease within 6 months from the end of the therapy with a PI3K inhibitor

Willingness and ability to comply with study and follow-up procedures, and give written informed consent

Female subjects of childbearing potential must be surgically sterile, be post-menopausal (per institutional guidelines), or must have a negative pregnancy test within 3 days prior to cycle 1 day 1 and agree to use medically acceptable contraception throughout the study period and for 4 months after the last dose of either study drug. Men of reproductive potential may not participate unless they agree to use medically acceptable contraception throughout the study period and for 4 months after the last dose of either study drug

Patients must be expected to receive at least 2 cycles of therapy

Patients should have an expected survival if untreated of \>= 90 days

Total bilirubin =\< 1.5 x upper limit of normal (ULN) (\< 3 x ULN for patients with Gilbert-Meulengracht syndrome or for patients with cholestasis due to compressive adenopathies of the hepatic hilum) (collected no more than 7 days before starting study treatment)

Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x ULN (=\< 5 x ULN for patients with liver involvement by lymphoma (collected no more than 7 days before starting study treatment)

Lipase =\< 1.5 x ULN (collected no more than 7 days before starting study treatment)

International normalized ratio (INR) =\< 1.5 and partial thromboplastin time (PTT) =\< 1.5 x ULN. PT can be used instead of INR if =\< 1.5 x ULN (collected no more than 7 days before starting study treatment)

Platelet count \>= 75,000 /mm\^3. For patients with lymphomatous bone marrow infiltration, platelet count \>= 50,000 /mm\^3 (collected no more than 7 days before starting study treatment)

Hemoglobin (Hb) \>= 8 g/dl (collected no more than 7 days before starting study treatment). Packed red blood cell transfusion or erythropoietin should not be given less than 7 days before the exam collection

Absolute neutrophil count (ANC) \>= 1,000/mm\^3 (collected no more than 7 days before starting study treatment). For patients with confirmed lymphomatous bone marrow infiltration, ANC count \>= 750/mm\^3. Myeloid growth factors should not be given less than 7 days before the exam collection

Previous or concurrent history of malignancies within 3 years prior to study. Any exceptions beyond those listed below must be approved by the principal investigator:

* Cervical carcinoma in situ

* Non-melanoma skin cancer

* Superficial bladder cancer (Ta \[non-invasive tumor\], Tis \[carcinoma in situ\] and T1 \[tumor invades lamina propria\])

* Localized prostate cancer

Active, clinically serious infections (\> Common Terminology Criteria for Adverse Events \[CTCAE\] grade 2)

Known hypersensitivity to any of the study drugs, study drug classes, or excipients in the formulation.

Proteinuria of \>= CTCAE grade 3 as assessed by a 24 hour (h) total urine protein quantification or estimated by urine protein: creatinine ratio \> 3.5 on a random urine sample

Unresolved toxicity from prior therapy higher than National Cancer Institute (NCI)-CTCAE grade 1 attributed to any prior therapy/procedure excluding alopecia or sensory neuropathy. Concurrent diagnosis of pheochromocytoma

Pregnant or breast-feeding patients. Women of childbearing potential must have a pregnancy test performed a maximum of 7 days before start of treatment, and a negative result must be documented before start of treatment

Substance abuse, medical, psychological or social conditions that may interfere with the patient's participation in the study or evaluation of the study result

Congestive heart failure \> New York Heart Association (NYHA) class 2

Unstable angina (angina symptoms at rest), new-onset angina (begun within the last 3 months)

Myocardial infarction less than 6 months before start of test drug

Uncontrolled arterial hypertension despite optimal medical management (per investigator's assessment)

Arterial or venous thrombotic or embolic events such as cerebrovascular accident (including transient ischemic attacks), deep vein thrombosis or pulmonary embolism within 3 months before the start of study treatment

Non-healing wound, ulcer, or bone fracture

Active, clinically serious infections \> CTCAE grade 2

Patients with seizure disorder requiring medication

Patients with evidence or history of bleeding diathesis. Any hemorrhage or bleeding event \>= CTCAE grade 3 within 4 weeks prior to the start of study treatment

Any illness or medical conditions that are unstable or could jeopardize the safety of the patients and their compliance in the study

History of having received an allogeneic bone marrow or organ transplant

Anti-arrhythmic therapy (beta blockers or digoxin are permitted)

Major surgical procedure or significant traumatic injury (as judged by the investigator) less than 28 days before start of treatment, open biopsy less than 7 days before start of treatment

Systemic continuous corticosteroid therapy at a daily dose higher than 15 mg prednisone or equivalent is not allowed. Patients may be using topical or inhaled corticosteroids. Previous corticosteroid therapy must be stopped or reduced to the allowed dose at least 7 days performing the screening computed tomography (CT)/magnetic resonance imaging (MRI). If a patient is on chronic corticosteroid therapy, corticosteroids should be de-escalated to the maximum allowed dose before the screening. Patients may be using topical or inhaled corticosteroids

Use of CYP3A4 inhibitors and inducers. Copanlisib is primarily metabolized by CYP3A4. Therefore, concomitant use of strong inhibitors of CYP3A4 (e.g., ketoconazole, itraconazole, clarithromycin, ritonavir, indinavir, nelfinavir and saquinavir), and strong inducers of CYP3A4 (e.g., rifampin, phenytoin, carbamazepine, phenobarbital, St. John's wort) are not permitted from day -14 of cycle 1 until the safety follow-up visit

What this study is about