Inclusion Criteria:
* Patients with histologically documented advanced or metastatic solid tumors with relapsed or refractory disease who have received standard-of-care or approved therapies known to confer clinical benefit, or patients with aggressive lymphomas who have received ≥ 2 prior lines of lymphoma-directed therapy and who do not have remaining effective treatment options (including transplant). Additionally, patients with indolent lymphomas must meet criteria for treatment.
* Patients must have measurable or evaluable disease
* Age \>= 18 years
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2
* Hemoglobin \>= 9 g/dL (patients may be transfused to achieve this value; elevated indirect bilirubin due to post-transfusion hemolysis is allowed)
* Absolute neutrophil count \>= 1,000/mcL
* Platelets \>= 75,000/mcL
* 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 \[SGPT\]) =\< 3 x institutional ULN OR =\< 5 x institutional upper limit of normal for patients with liver metastases at baseline
* Creatinine =\< 1.5 x institutional ULN OR creatinine clearance \>= 60 mL/min/1.73 m\^2 by Cockcroft-Gault
* Any prior therapy must have been completed \>= 4 weeks, or \>= 5 half-lives of the prior agent (whichever is shorter) prior to enrollment on protocol. Prior definitive radiation should have been completed \>= 4 weeks prior to enrollment; prior palliative radiation should have been completed \>= 2 weeks prior to enrollment. 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) and should have recovered to grade 1 or baseline from any toxicities
* Female patients who:
* Are postmenopausal (age-related amenorrhea \>= 12 consecutive months or follicle-stimulating hormone \> 40 mIU/mL), for at least 1 year before the screening visit, OR
* Are surgically sterile (i.e., who had undergone hysterectomy or bilateral oophorectomy), OR
If they are of childbearing potential:
* Agree to practice 1 highly effective method and 1 additional effective (barrier) method of contraception, at the same time, from the time of signing the informed consent through 4 months after the last dose of study drug (female and male condoms should not be used together), or
* Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[e.g., calendar, ovulation, symptothermal, postovulation methods\] withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception.)
* Male patients, even if surgically sterilized (i.e., status postvasectomy), who:
* Agree to practice effective barrier contraception during the entire study treatment period and through 4 months after the last dose of study drug (female and male condoms should not be used together), or
* Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[eg, calendar, ovulation, symptothermal, postovulation methods for the female partner\] withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception.)
* The effects of TAK-243 on the developing human fetus are unknown. For this reason and because ubiquitin-activating enzyme inhibitors are known to be teratogenic, 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 and for the duration of study participation. 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 TAK-243 administration
* Ability to understand and the willingness to sign a written informed consent document
* Willingness to provide blood for research purposes
* For expansion phase patients, willingness to undergo 2 core needle biopsy procedures for research purposes if there is a lesion or lesions amenable to repeat biopsy
* Patients on anticoagulation therapy are eligible for this study in the absence of anticipated drug-drug interactions (DDI) between the anticoagulation agent and TAK-243. If DDI are anticipated and another anticoagulation agent that is compatible with TAK-243 exists, the patient will be transitioned to this alternative, TAK-243-compatible anticoagulation agent
Exclusion Criteria:
* Patients who are receiving any other investigational agents
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection or psychiatric illness/social situations that would limit compliance with study requirements
* Life-threatening illness unrelated to cancer
* Patients with uncontrolled coagulopathy or bleeding disorder
* Known hepatic cirrhosis or severe pre-existing hepatic impairment
* Known cardiopulmonary disease defined as:
* Unstable angina pectoris;
* Congestive heart failure (New York Heart Association \[NYHA\] class III or IV);
* Myocardial infarction (MI) within 6 months prior to first dose (patients who had ischemic heart disease such as a \[acute coronary syndrome (ACS)\], MI, and/or revascularization greater than 6 months before screening and who are without cardiac symptoms may enroll);
* Cardiomyopathy
* Clinically significant arrhythmia:
* History of polymorphic ventricular fibrillation or torsade de pointes,
* Permanent atrial fibrillation (a fib), defined as continuous a fib for \>= 6 months,
* Persistent a fib, defined as sustained a fib lasting \> 7 days and/or requiring cardioversion in the 4 weeks before screening,
* Grade 3 a fib defined as symptomatic and incompletely controlled medically, or controlled with device (e.g., pacemaker) or ablation, and
* Patients with paroxysmal a fib or \< grade 3 a fib for period of at least 6 months are permitted to enroll provided that their rate is controlled on a stable regimen
* Prolonged rate corrected QT (QTc) interval \>= 470 m/sec, calculated according to institutional guidelines
* Uncontrolled high blood pressure (i.e., systolic blood pressure \> 180 mm Hg, diastolic blood pressure \> 95 mm Hg)
* Known moderate to severe chronic obstructive pulmonary disease, interstitial lung disease, and pulmonary fibrosis
* Major surgery within 14 days before the first dose of any study drug
* Female patients who intend to donate eggs (ova) during the course of this study or 4 months after receiving their last dose of study drug(s)
* Male patients who intend to donate sperm during the course of this study or 4 months after receiving their last dose of study drug(s)
* 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
* TAK-243 is primarily metabolized by CYP3A4/5. Therefore, the concomitant use of strong inhibitors of CYP3A4/5 (e.g., ketoconazole, itraconazole, clarithromycin, ritonavir, indinavir, nelfinavir and saquinavir) and strong inducers of CYP3A4/5 (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
* TAK-243 is a substrate for both organic anion transporting polypeptides (OATP) in human hepatocytes and the drug efflux transporter BCRP (ABCG2). Therefore, concomitant use of drugs that are strong inhibitors of BCRP or OATP is not permitted from 14 days prior to enrollment until the end of the study
* Other medications that are prohibited while on TAK-243 treatment include herbal medications/preparations (except for vitamins). Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated medical reference for a list of drugs to avoid or minimize use of
* As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product
* Patients undergoing vaccination with live vaccines and live attenuated vaccines in the 30 days prior to receiving TAK-243, during the study, and for 100 days after the last dose of study drug. Inactivated vaccines are permitted
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to TAK-243
* Patients with evidence of chronic hepatitis B virus (HBV) infection who are currently on treatment are eligible if they have an undetectable HBV viral load
* Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load
* Known human immunodeficiency virus (HIV)-positive patients who meet the following criteria will be considered eligible:
* CD4 count \> 350 cells/mm\^3
* Undetectable viral load for 6 months prior to enrollment
* Maintained on modern therapeutic regimens utilizing non-CYP-interactive agents
* No history of acquired immunodeficiency syndrome (AIDS)-defining opportunistic infections
* Pregnant and lactating/breast-feeding women are excluded from this study because TAK-243 is a UAE-inhibiting agent with the potential for teratogenic or abortifacient effects and there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with TAK-243
