Phase 2 Study of AT13387 (Onalespib) in ALK+ ALCL, MCL, and BCL-6+ DLBCL

Inclusion Criteria:

* Patients must have histologically confirmed, relapsed/refractory ALK+ ALCL (with ALK positivity defined by immunohistochemistry and/or fluorescence in situ hybridization \[FISH\]/cytogenetics from any prior biopsy), MCL, or BCL6+ DLBCL (with BCL6 positivity defined by immunohistochemistry from any prior biopsy) and meet the following criteria:
* Patients must have measurable disease that has not been previously irradiated, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm (\>= 2 cm) with conventional imaging or \>= 10 mm with spiral computed tomography (CT) scan; if the patient has been previously irradiated, there must be evidence of progression since the radiation

  * Please note, this trial includes mandatory tumor biopsies pre-treatment, during cycle 1 and at the time of disease progression of accessible tumor; having accessible tumor for biopsy is not required for eligibility; we expect that at least 80% of patients will have accessible tumor for these biopsies, however
* Prior therapy

  * Please note, the washout period for prior therapies cannot be shortened
  * Please note, prior therapies can be from any time in the past
* ALK+ ALCL: patients must have disease that has relapsed and or is refractory to prior therapy, which must have included a multiagent chemotherapy regimen including an anthracycline, if not contraindicated, and prior brentuximab; prior crizotinib or other ALK inhibitor therapy, while recommended, is not mandatory; patients must have relapsed following or be ineligible for, or refuse, autologous stem cell transplant
* MCL: patients must have disease that has relapsed and or is refractory to prior therapy, which must have included a multiagent chemotherapy regimen and prior ibrutinib or other BTK inhibitor therapy; patients must have relapsed following or be ineligible for, or refuse, autologous stem cell transplant
* BCL6+ DLBCL: patients must have disease that has relapsed and or is refractory to prior therapy, which must have included an anthracycline, if not contraindicated; patients must have relapsed following or be ineligible for, or refuse, autologous stem cell transplant
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)
* Life expectancy of greater than 3 months
* Absolute neutrophil count \>= 1,000/mcL
* Platelets \>= 75,000/mcL, unless due to marrow involvement by lymphoma in which case a platelet count of \>= 30,000/mcL will be used
* Total bilirubin =\< 1.5 x upper limit of normal (ULN), unless due to Gilbert's syndrome or hemolysis, in which case =\< 3.0 x ULN is allowed
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3.0 x institutional upper limit of normal
* Creatinine =\< 1.5 x ULN or a creatinine clearance \>= 50 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal
* Potassium above the institutional lower limit of normal (supplementation to meet this is allowed)
* Magnesium above the institutional lower limit of normal (supplementation to meet this is allowed)
* Human immunodeficiency virus (HIV)+ patients are eligible for the trial provided they meet the other study criteria in addition to the following:

  * CD4+ T-cells \>= 250/mm\^3
  * HIV sensitive to antiretroviral therapy
  * Zidovudine not allowed
  * Long term survival anticipated on the basis of HIV alone were it not for the lymphoma
  * No concurrent acquired immunodeficiency syndrome (AIDS)-defining illness other than the lymphoma
* The effects of AT13387 (onalespib) on the developing human fetus are unknown; for this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 4 months after the completion of AT13387 (onalespib) administration; 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 the study, for the duration of study participation, and 4 months after completion of AT13387 (onalespib) administration
* Although the pharmacokinetic (PK) data in humans is still unknown, the potential for drug-interaction cannot be ruled out; pre-clinical studies suggest that AT13387 (onalespib) is a substrate of P-glycoprotein (P-gp), a moderate inhibitor of BCRP and P-gp, and a strong inhibitor of MATE 1/2-K; patients must be willing to not take St. John wort or grapefruit juice while participating in this trial and should avoid drugs that are strong inducers of P-gp, and to switch to alternative drugs when available
* Hepatitis B positive patients are eligible; prophylactic hepatitis B virus (HBV) therapy is recommended but only if there is no circulating virus detectible
* Transformed lymphoma patients are eligible
* Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

* Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier; steroids for symptom palliation are allowed, but must be either discontinued or on stable doses at the time of initiation of protocol therapy
* Patients who are receiving any other investigational agents; all investigational agents other than ibrutinib must have been discontinued at least 4 weeks prior to beginning treatment; prior ibrutinib therapy must have been discontinued at least 2 weeks prior to beginning therapy
* Patients with known leptomeningeal or brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events; imaging or spinal fluid analysis to exclude central nervous system (CNS) involvement is not required, unless there is clinical suspicion by the treating investigator
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to AT13387 (onalespib)
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements

  * There will be no exclusion of patients with known visual impairment or symptoms, including by not limited to peripheral flashes (photopsia), blurred or double vision, floaters, color distortion and dimness, difficulties with light/dark accommodation, tunnel vision or other field defects, halos, apparent movement of stationary objects, and complex disturbances; patients will have a baseline ophthalmologic exam to serve as a point of comparison and further exams as needed should visual symptoms develop; no pretreatment eye exam findings or ocular symptoms have been associated with an increased risk of ocular toxicity seen with AT13387
* Pregnant women are excluded from this study because AT13387 (onalespib) has the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with AT13387 (onalespib), breastfeeding should be discontinued if the mother is treated with AT13387 (onalespib)
* Patients, who have had a major surgery or significant traumatic injury within 4 weeks of start of study drug, patients who have not recovered from the side effects of any major surgery (defined as requiring general anesthesia) or patients that may require major surgery during the course of the study
* Prior history of another malignancy (except for non-melanoma skin cancer or in situ cervical or breast cancer) unless disease free for at least three years; patients with prostate cancer are allowed if prostate specific antigen (PSA) is less than 1
* Patients should not receive immunization with attenuated live vaccine within one week of study entry or during study period
* History of noncompliance to medical regimens
* Consistent corrected QT (QTc) \> 450 msec for men and \> 470 msec for women by Fridericia formula, on 3 separate electrocardiograms (ECGs)
* Left ventricular ejection fraction (LVEF) \< 50%, regardless of whether there are symptoms of heart failure