Navitoclax and Vistusertib in Treating Patients With Relapsed Small Cell Lung Cancer and Other Solid Tumors

Inclusion Criteria: * PHASE 1 SPECIFIC ELIGIBILITY CRITERIA * Patients must have histologically or cytologically confirmed malignancy that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective * PHASE 2 SPECIFIC ELIGIBILITY CRITERIA * Patients must have histologically or cytologically confirmed small cell lung cancer whose disease has relapsed or progressed after \>= 1 prior therapy, one of which must have been a platinum doublet; pathology confirmation must be done at Sidney Kimmel Comprehensive Cancer Center (SKCCC) or at the local participating site * Patients must have measurable disease, 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) by chest x-ray or as \>= 10 mm (\>= 1 cm) with computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam * Subjects must be willing to undergo 2 sets of core needle biopsies (pre-treatment and on-treatment), if there are lesions amenable to biopsy; an optional core biopsy will be requested at progression * GENERAL ELIGIBILITY CRITERIA * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 70%) * Life expectancy of greater than 12 weeks * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Hemoglobin \>= 9.0 g/dL * Platelets \>= 100,000/mcL * Activated partial thromboplastin time (aPTT), prothrombin time (PT) =\< 1.2 x upper limit of normal (ULN) * Total bilirubin =\< 1.5 x ULN (patients with Gilbert's syndrome may have serum bilirubin \> 1.5 ULN) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional ULN if no demonstrable liver metastases or =\< 5 x ULN in the presence of liver metastases * Creatinine =\< 1.5 x ULN and concurrent creatinine clearance (CrCl) \>= 50 mL/min/1.73 m\^2 for patients with creatinine (Cr) \> 1.5 x ULN * Proteinuria \< 1+ on dipstick testing (if 2+ seen on first test, retest \>= 24 hours later) * Patients with a history of central nervous system (CNS) metastases must have documentation of stable or improved status based on brain imaging for at least 2 weeks after completion of definitive treatment and within 2 weeks prior to first dose of study drug, off or on a stable dose of corticosteroids * Patients must have completed chemotherapy, biological or radiotherapy \>= 3 weeks prior to entering the study * Patients must have recovered to =\< grade 1 adverse events or to =\< grade 2 alopecia and sensory neuropathy due to prior treatment * Patients must be able to understand and the willingness to sign a written informed consent document * Patients must be able to swallow pills * The effects of navitoclax and vistusertib on the developing human fetus are unknown; for this reason, women of child-bearing potential and men must agree to use adequate contraception prior to study entry, for the duration of study participation, and up to 90 days following completion of therapy; for women this should include one highly effective method of contraception and one barrier method as defined below * Highly effective methods include: * Total abstinence from sexual intercourse (minimum one complete menstrual cycle prior to study drug administration); * Vasectomized partner; * Medroxyprogesterone acetate depot injection; * Placement of a copper-banded intrauterine device (IUD) or intrauterine system (IUS); * Bilateral tubal ligation; * Barrier methods include: * Condom; * Occlusive cap (e.g. diaphragm or cervical/vault caps) with spermicide * Please note: use of other oral, injected or implanted hormonal methods of contraception cannot be considered highly effective as it is currently unknown whether vistusertib may reduce their effectiveness; periodic abstinence, the rhythm method, and the withdrawal method are not acceptable methods of contraception * Additionally, male subjects (including those who are vasectomized) whose partners are pregnant or might be pregnant must agree to use condoms for the duration of the study and for 90 days following completion of therapy * Women of childbearing potential must have a negative urine pregnancy test within 7 days prior to initiation of treatment, women will be considered not of childbearing potential if they are surgically sterile (bilateral oophorectomy or hysterectomy) and/or post-menopausal (amenorrheic for at least 12 months) * 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 for 90 days after completion of navitoclax and/or vistusertib administration Exclusion Criteria: * PHASE 2 SPECIFIC EXCLUSION CRITERIA * Prior treatment with a TORC1, dual TORC1/2 inhibitor, or BCL-2/xL inhibitor * Patients with active malignancies other than SCLC or patients with prior curatively treated malignancy at high risk of relapse during the study period with the exception of localized squamous or basal cell skin cancers * PHASE 1 AND GENERAL EXCLUSION CRITERIA * Major surgery within 21 days of starting protocol treatment * Patients who are receiving any other investigational agents * History of allergic reactions attributed to compounds of similar chemical or biologic composition to navitoclax or vistusertib * Patients receiving anticoagulation or anti-platelet therapy are excluded due to the risk of thrombocytopenia with navitoclax * Excluded agents include heparin or low molecular weight heparin, warfarin, clopidogrel, ibuprofen and other non-steroidal anti-inflammatory drugs (NSAIDS), tirofiban, and other anticoagulants, drugs, or herbal supplements that affect platelet function * Administration of heparin to keep subject's infusion lines patent is allowed; low-dose anticoagulation medications that are used to maintain the patency of a central intravenous catheter are allowed * Aspirin will not be allowed within 7 days prior to the first dose of navitoclax or during navitoclax administration; however, subjects who have previously received aspirin therapy for thrombosis prevention, may resume a low dose (i.e., maximum 100 mg once daily \[QD\]) of aspirin if platelet counts are stable (\>= 50,000/mm3) through 6 weeks of navitoclax administration * All decisions regarding treatment with aspirin therapy will be determined by the investigator in conjunction with the medical monitor * Patients with an underlying condition predisposing them to bleeding or currently exhibiting signs of clinically significant bleeding * Patients with a recent history of non-chemotherapy-induced thrombocytopenic-associated bleeding within 1 year prior to the first dose of study drug * Patients with a significant history of cardiovascular disease or procedures within the preceding 6 months (e.g., myocardial infarction \[MI\], coronary artery bypass graft placement, angioplasty, vascular stent, angina pectoris, ventricular arrhythmias requiring continuous therapy, congestive heart failure New York Heart Association \[NYHA\] grade \>= 2, thrombotic or thromboembolic event) * Any of the following cardiac criteria: * Mean resting corrected QT interval (QTc using Fridericia's formula \[QTcF\]) \> 470 msec obtained from 3 electrocardiograms * Congenital or family history of long or short QT syndrome, Brugada syndrome, known history of QTc prolongation or torsades de pointes within 12 months of entering the study * Abnormal echocardiogram at baseline (left ventricular ejection fraction \[LVEF\] \< 40% and shortening fraction \[SF\] \< 15%) * Drugs which have an increased risk for QTc prolongation should be avoided * Patients with uncontrolled type 1 or type 2 diabetes. Vistusertib belongs to a class of drugs that causes hyperglycemia. In order to assess toxicity, patients with an elevated risk of hyperglycemia should be excluded from study * Patients currently receiving medications or herbal supplements of the classes below are ineligible; patients are eligible if they stop use of these compounds at least 1 week prior to receiving any treatment on this protocol * Potent inhibitors or inducers of CYP3A4 /5 (CYP3A4 inhibitors such as ketoconazole and clarithromycin are not allowed 7 days prior to the first dose of navitoclax and during navitoclax administration) * Strong or moderate inhibitors of Pgp or BRCP1 * Sensitive substrates of CYP2C9 (i.e. phenytoin and warfarin) * Substrates of certain drug transporters (OATP1B1, OATP1B3, MATE1 or MATE2K) * Pregnant women are excluded from this study because navitoclax and vistusertib have 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 navitoclax and vistusertib breastfeeding should be discontinued if the mother is treated with navitoclax and vistusertib * Patients positive for human immunodeficiency virus (HIV) are not excluded from this study, but HIV-positive patients must have: * A stable regimen of highly active anti-retroviral therapy (HAART) that does not include strong or moderate CYP3A4 inducers or inhibitors * No requirement for concurrent antibiotics or antifungal agents for the prevention of opportunistic infections * A CD4 count above 250 cells/mcL and an undetectable HIV viral load on standard polymerase chain reaction (PCR)-based test * Any hematopoietic growth factors (e.g., filgrastim \[granulocyte colony-stimulating factor; G-CSF\], sargramostim \[granulocyte-macrophage colony-stimulating factor; GM-CSF\]) within 14 days prior to receiving study treatment * 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 * Patients who have received a live, attenuated vaccines within 4 weeks of first dose of drug