Testing Proton Craniospinal Radiation Therapy Versus the Usual Radiation Therapy for Leptomeningeal Metastasis, RADIATE-LM Trial

Inclusion Criteria: * PRIOR TO STEP 1 REGISTRATION * Patients with pathologically (histologically or cytologically) proven diagnosis of breast cancer or NSCLC * Patients must have newly diagnosed leptomeningeal metastasis established through at least one of the following: * Positive CSF cytology for malignancy * CSF cytology with suspicious cells is considered positive; CSF cytology with atypical cells is considered equivocal and not positive * Patients with an equivocal or negative CSF cytology result, or not suitable for CSF sampling, radiographic diagnosis of leptomeningeal metastasis with linear and/or nodular disease and documentation of typical clinical signs (European Association of Neuro-Oncology \[EANO\]-European Society for Medical Oncology \[ESMO\] Diagnostic Criteria Type IIA-IIC) is required * Patients with typical clinical signs of leptomeningeal metastasis may have one or more of the following symptoms and signs: headache, nausea, vomiting, mental status change, gait difficulty, cranial nerve palsy, diplopia, visual change, hearing loss, radicular weakness, radicular sensory change, urinary retention, saddle anesthesia, constipation, neck pain, and back pain * For patients with prior history of immunotherapy or current immunotherapy, CSF sampling rather than just MRI enhancement is strongly recommended to exclude immune-related aseptic meningitis * Patients must be candidates for radiation therapy for the treatment of leptomeningeal metastasis * Age ≥ 18 * PRIOR TO STEP 2 REGISTRATION * Note: Step 2 registration must occur no later than 30 calendar days after step 1 registration * Financial clearance for proton therapy treatment * Patients must have systemic disease evaluation through standard of care imaging for example CT chest/abdomen/pelvis or body PET/CT * Karnofsky performance status ≥ 60 * Not pregnant and not nursing * Negative urine or serum pregnancy test (in persons of childbearing potential) within 14 days prior to registration. Childbearing potential is defined as any person who has experienced menarche and who has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy) or who is not postmenopausal * Hemoglobin ≥ 8.0 g/dl (Note: The use of transfusion or other intervention to achieve hemoglobin \[Hgb\] ≥ 8.0 g/dl is acceptable) * Absolute neutrophil count (ANC) ≥ 1,000/mm\^3 (Note: the use of granulocyte-colony stimulating factor or other intervention to achieve ANC ≥ 1,000/mm\^3 is acceptable) * Platelets ≥ 100,000/mm\^3 (Note: the use of transfusion or other intervention to achieve platelets ≥ 100,000/mm\^3 is acceptable) * Total bilirubin ≤ 1.5 × institutional upper limit of normal (ULN) (patients with known Gilbert disease without other clinically significant liver abnormalities are not excluded) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine transaminase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) ≤ 3 × ULN * No prior radiation therapy to the spinal cord with equivalent dose in 2 gray (Gy) fractions (EQD2) more than 40Gy or cauda equina with EQD2 more than 50Gy using alpha/beta ratio of 3 * No prior treatment for leptomeningeal metastasis (note: prior CNS treatment for other non-leptomeningeal disease is allowed) * No history of unstable angina requiring hospitalization in the last 3 months * No history of myocardial infarction within the last 3 months * New York Heart Association Functional Classification II or better (New York Heart Association \[NYHA\] Functional Classification III/IV are not eligible) (Note: Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification.) * No active infection currently requiring intravenous (IV) antibiotic management * No active chronic obstructive pulmonary disease exacerbation or other acute respiratory illness precluding study therapy * No CTCAE v5.0 ≥ grade 2 encephalopathy