Direct Tumor Microinjection and FDG-PET in Testing Drug Sensitivity in Patients With Relapsed or Refractory Non-Hodgkin Lymphoma, Hodgkin Lymphoma, or Stage IV Breast Cancer

Inclusion Criteria: * Age \>= 18 years * Histologically proven of relapsed or refractory * Non-Hodgkin lymphoma (NHL) or Hodgkin lymphoma (HL) nodal or extranodal mass OR * Cutaneous T-cell lymphoma (CTCL) including mycosis fungoides (MF), as well as transformed MF OR * Breast adenocarcinoma with nodal or cutaneous metastases (stage 4) * NOTE: Patients must be refractory to or intolerant of existing therapy(ies) known to provide clinical benefit for their condition * NOTE: The patient must not be a candidate for any curative therapy or any known life-prolonging therapy * Cohort I: For nodal/extranodal mass, presence of lesions that are amenable for injections as determined by interventional radiology * NOTE: Nodal or extranodal mass must be palpable and easily accessible; masses such as mediastinum, retroperitoneum, within solid organs, spinal sites, central nervous system (CNS) sites, etc., are NOT allowed * Measurable disease: * For nodal or extranodal disease (lymphoma or breast): must have at least 2 lesions that are \>= 20 mm (2.0 cm) in the longest diameter by physical exam and/or on cross-sectional imaging and measurable in two perpendicular dimensions per computed tomography PET-computed tomography (CT); For Cohort I, the lesions must be amenable to intralesional injections as determined by interventional radiology (including tumors that can be safely accessed using imaging guidance and treated with minimal risk to adjacent structures) * For cutaneous lesions (lymphoma or breast): at least two visible, non-infected skin lesions that are greater than 1 cm and are amenable to intralesional injection as determined by investigator * Candidate for further therapy and able to wait 7 days prior to start of next systemic therapy * Absolute neutrophil count (ANC) \>= 1000/mm\^3 (obtained =\< 14 days prior to registration) * Platelet count \>= 50,000/mm\^3 (obtained =\< 14 days prior to registration) * International normalized ratio (INR)/prothrombin time (PT) =\< 1.5 (obtained =\< 14 days prior to registration) * Negative serum or urine pregnancy test done =\< 7 days prior to registration, for persons of childbearing potential only * Provide written informed consent * Willing to return to enrolling institution for follow-up * Willing to provide tissue samples for correlative research purposes Exclusion Criteria: * Any of the following: * Pregnant persons * Nursing persons * Persons of childbearing potential who are unwilling to employ adequate contraception * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens * Systemic corticosteroids between pre-PET and post-PET evaluation and biopsy * Prohibited treatments and or therapies * Autologous stem cell transplant (ASCT) =\< 12 weeks prior to registration * Prior chemotherapy =\< 2 weeks prior to registration * Prior treatment with nitrosureas =\< 4 weeks prior to registration * Therapeutic anticancer antibodies =\< 2 weeks prior to registration * Radio- or toxin immunoconjugates =\< 4 weeks prior to registration * Radiation therapy to the injected area =\< 2 weeks prior to registration * Major surgery =\< 2 weeks prior to registration * Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm * Requires anticoagulation that cannot be discontinued prior to biopsy * Note: Exception if able to hold antiplatelet agents 7 days prior to the injections and biopsy * NOTE: Low molecular weight heparin (LMWH) will be allowed for bridging if on warfarin * NOTE: Heparin for line patency without detectable lab abnormalities for coagulation will be allowed