Ulixertinib in Treating Patients With Advanced Solid Tumors, Non-Hodgkin Lymphoma, or Histiocytic Disorders With MAPK Pathway Mutations (A Pediatric MATCH Treatment Trial)

Inclusion Criteria: * Patient must have enrolled onto APEC1621SC and must have been given a treatment assignment to MATCH to APEC1621J based on the presence of an actionable mutation. * Patients must have a body surface area \>= 0.54 m\^2 at the time of study enrollment. * Patients must have radiographically measurable disease at the time of study enrollment. Patients with neuroblastoma who do not have measurable disease but have metaiodobenzylguanidine (MIBG)+ evaluable disease are eligible. Measurable disease in patients with central nervous system (CNS) involvement is defined as tumor that is measurable in two perpendicular diameters on magnetic resonance imaging (MRI) and visible on more than one slice. * Note: The following do not qualify as measurable disease: * Malignant fluid collections (e.g., ascites, pleural effusions) * Bone marrow infiltration except that detected by MIBG scan for neuroblastoma * Lesions only detected by nuclear medicine studies (e.g., bone, gallium or positron emission tomography \[PET\] scans) except as noted for neuroblastoma * Elevated tumor markers in plasma or cerebrospinal fluid (CSF) * Previously radiated lesions that have not demonstrated clear progression post radiation * Leptomeningeal lesions that do not meet the measurement requirements for Response Evaluation Criteria in Solid Tumors (RECIST) 1.1. * Karnofsky \>= 50% for patients \> 16 years of age and Lansky \>= 50 for patients =\< 16 years of age. Note…