Inclusion Criteria:
* Patients with histologically documented metastatic, recurrent, or locally unresectable solid tumors which have progressed after one line of therapy, or for which no curative therapy is available. Patients with lymphoma who have received adequate exposure to standard of care therapy and for whom no curative therapy is available are also eligible (this trial will enroll a minimum of 5 lymphoma patients)
* Patients must have measurable or evaluable disease
* Age \>= 18 years
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2
* Leukocytes \>= 2,000/mcL
* Absolute neutrophil count \>= 1,500/mcL
* Platelets \>= 100,000/mcL (solid tumor patients) \>= 75,000/mcL (lymphoma patients)
* Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN)
* Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) /alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) =\< 2.5 x institutional ULN
* Serum creatinine =\< 1.5 x institutional ULN OR creatinine clearance \>= 50 mL/min/1.73 m\^2 by Cockcroft-Gault
* Any prior therapy must have been completed \>= 4 weeks (6 weeks for nitrosoureas and mitomycin C) or, if known, \>= 5 half-lives of the prior agent (whichever is shorter) prior to enrollment on protocol (minimum of 1 week between prior therapy and study enrollment), and the participant must have recovered to eligibility levels from prior toxicity; prior definitive radiation should have been completed \>= 4 weeks or palliative radiation should have been completed \>= 2 weeks prior to study enrollment and all associated toxicities resolved to eligibility levels (patients on study may be eligible for palliative radiotherapy to non-targeted lesions after 2 cycles of therapy at the principal investigator's \[PI's\] discretion); patients must be \>= 2 weeks since any investigational agent administered as part of a phase 0 study (where a sub-therapeutic dose of drug is administered) at the PI's discretion, and should have recovered to grade 1 or baseline from any toxicities
* Patients who have had prior monoclonal antibody therapy must have completed that therapy \>= 6 weeks (or 3 half-lives of the antibody, whichever is shorter) prior to enrollment on protocol (minimum of 1 week between prior therapy and study enrollment)
* Patients who are therapeutically treated with an agent such as warfarin or heparin will be allowed to participate provided that their medication dose is stable, and international normalized ratio/partial thromboplastin time (INR/PTT) remains stable within the recommended therapeutic range
* Patients must have left ventricular ejection fraction (LVEF) \>= 50%
* The effects of nivolumab, copanlisib and ipilimumab on the developing human fetus are unknown, and there is potential for teratogenic or abortifacient effects. For this reason, women of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, during the treatment portion of the study, and for a minimum of 5 months after the last dose of study drug. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to study entry, for the duration of study participation, and for 7 months after completion of study treatment
* Ability to understand and the willingness to sign a written informed consent document
* Willingness to provide blood for research purposes (all patients, apart from patients enrolled onto triplet safety run-in phase) and willingness to provide new tumor biopsy samples for research purposes (doublet and triplet expansion cohorts)
Exclusion Criteria:
* Patients who are receiving any other investigational agents
* Patients with clinically significant illnesses which would compromise participation in the study, including but not limited to active or uncontrolled infection, immune deficiencies, hepatitis B, hepatitis C, active tuberculosis, uncontrolled asthma, symptomatic congestive heart failure, unstable angina pectoris, uncontrolled cardiac arrhythmia, myocardial infarction within the past 6 months, cerebral vascular accident/stroke within the past 6 months, or psychiatric illness/social situations that would limit compliance with study requirements
* Patients with known brain metastases or carcinomatous meningitis are excluded from this clinical trial, with the exception of patients whose brain metastatic disease status has remained stable for \>= 1 month after treatment of the brain metastases; patients on anti-seizure medications may be enrolled at the discretion of the principal investigator
* Patients with blood oxygen saturation \< 90% at rest; patients must not have symptomatic interstitial lung disease, pneumonitis, or known pulmonary fibrosis. Patients must also not have a history of interstitial lung disease of any severity
* Patients with uncontrolled arterial hypertension are ineligible. Uncontrolled arterial hypertension is defined as an average blood pressure of \> 140 mm Hg systolic and/or \> 90 mm Hg diastolic over 3 measurements, taken over the course of one clinic visit at intervals of \>=30 minutes. Patients with well-controlled arterial hypertension are eligible
* Patients with uncontrolled Type I or II diabetes mellitus, defined as fasting blood glucose of \> 160 mg/dL and glycosylated hemoglobin measurement (HgA1c) \> 8.5%, are ineligible. Patients with fasting blood glucose \>160 mg/dL may be eligible if the HgA1c \< 8.5%, per PI discretion. Patients with well-controlled diabetes mellitus are eligible
* Patients are not eligible if they have had or are planned for solid organ transplant or allogeneic hematopoietic stem cell transplant
* Patients should be excluded if they have a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration; however, systemic corticosteroids may be indicated after starting the study drugs to treat immune-related adverse reactions; inhaled or topical steroids and adrenal replacement doses =\< 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease
* Doublet cohort and triplet safety run-in phase: Patients are not eligible if they have had prior treatment with an anti-PD-1, anti-PD-L1, anti-PD-L2, or anti-CTLA-4 antibody, or any other antibody or drug specifically targeting immune checkpoint pathways. Patients should therefore be excluded if they have had prior treatment with the combination of a PI3K inhibitor and a PD-1 inhibitor; however, prior treatment with a PI3K/AKT/mTOR inhibitor (without the addition of a checkpoint inhibitor) is allowed. Patients that have had prior chimeric antigen receptor (CAR) T-cell therapy are eligible
* Triplet pharmacodynamic phase only: Patients who have previously received one line of immunotherapy (including checkpoint inhibitors) are eligible; however, patients previously receiving ipilimumab + nivolumab combination therapy are excluded. Patients who received prior therapy with a checkpoint inhibitor and were taken off drug for serious adverse events are excluded. Prior treatment with a PI3K/AKT/mTOR inhibitor, or prior CAR T-cell therapy is allowed
* Copanlisib is primarily metabolized by CYP3A4. Therefore, the 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) is not permitted from 14 days prior to enrollment until the end of the study. Other medications that are prohibited while on copanlisib treatment:
* Herbal medications/preparations (except for vitamins)
* Anti-arrhythmic therapy other than beta blockers or digoxin
* Human immunodeficiency virus (HIV)-positive patients are eligible if on stable dose of highly active antiretroviral therapy (HAART), no clinically significant drug-drug interactions are anticipated with the current HAART regimen, and viral load is undetectable. Patients on HAART regimens that include CYP3A4 inhibitors (e.g. ritonavir or cobicistat) are excluded. All patients must be screened for HIV up to 28 days prior to enrollment
* Hepatitis B (HBV) or hepatitis C (HCV) infection. All patients must be screened for HBV and HCV up to 28 days prior to enrollment using the routine hepatitis virus lab panel. Patients positive for hepatitis B virus surface antigen measurement (HBsAg) and/or hepatitis B virus core antibody measurement (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 ribonucleic acid (RNA)
* Cytomegalovirus (CMV) infection. All patients must be screened for CMV up to 28 days prior to enrollment. Patients that are positive for CMV DNA by polymerase chain reaction (PCR) are not eligible for the study
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to copanlisib, PI3K inhibitors, nivolumab, or ipilimumab
* Patients with active autoimmune disease requiring systemic treatment within the past 3 months, a documented history of clinically severe autoimmune disease, or a syndrome that requires systemic steroids or immunosuppressive agents are not eligible. Patients with vitiligo or resolved childhood asthma/atopy would be an exception to this rule. Patients that require intermittent use of bronchodilators or local steroid injections will not be excluded from the study. Patients with hypothyroidism and stable on hormone replacement or Sjogren's syndrome will not be excluded from the study
* Pregnant or breastfeeding women will be excluded from participation in this trial, as there is no significant preclinical information regarding the effects of nivolumab, copanlisib, and ipilimumab, on a fetus or newborn infant
