MORAb-004 in Treating Young Patients With Recurrent or Refractory Solid Tumors or Lymphoma

Inclusion Criteria: * Patients with relapsed or refractory solid tumors or lymphoma, excluding central nervous system (CNS) tumors, are eligible; patients must have had histologic verification of malignancy at original diagnosis or relapse; (patients with primary CNS tumors, known CNS metastases, or a prior history of CNS metastases are not eligible) * Patients must have either measurable or evaluable disease * Patient's current disease state must be one for which there is no known curative therapy or therapy proven to prolong survival with an acceptable quality of life * Karnofsky \>= 50% for patients \> 16 years of age and Lansky \>= 50 for patients =\< 16 years of age; Note: patients who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score * Patients must have fully recovered from the acute toxic effects of all prior anti-cancer chemotherapy * At least 21 days after the last dose of myelosuppressive chemotherapy (42 days if prior nitrosourea) * At least 14 days after the last dose of a long-acting growth factor (e.g. Neulasta) or 7 days for short-acting growth factor; for agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur; the duration of this interval must be discussed with the study chair * At least 7 days after the last dose of a biologic agent; for agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur; the duration of this interval must be discussed with the study chair * At least 42 days after the completion of any type of immunotherapy, e.g. tumor vaccines * At least 3 half-lives of the antibody after the last dose of a monoclonal antibody * At least 14 days after local palliative radiotherapy (XRT) (small port); at least 150 days must have elapsed if prior total-body irradiation (TBI), craniospinal XRT or if \>= 50% radiation of pelvis; at least 42 days must have elapsed if other substantial bone marrow (BM) radiation * No evidence of active graft vs. host disease and at least 56 days must have elapsed after transplant or stem cell infusion * For patients with solid tumors without known bone marrow involvement: * Peripheral absolute neutrophil count (ANC) \>= 1000/mm\^3 * Platelet count \>= 100,000/mm\^3 (transfusion independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment) * For patients with known bone marrow metastatic disease: * ANC \>= 750/mm\^3 * Platelet count \>= 75,000/mm\^3 (transfusion independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment) * Patients with known bone marrow metastatic disease will not be evaluable for hematologic toxicity; these patients must not be known to be refractory to red cell or platelet transfusion; at least 5 of every cohort of 6 patients with a solid tumor or lymphoma must be evaluable for hematologic toxicity; if dose-limiting hematologic toxicity is observed, all subsequent patients enrolled must be evaluable for hematologic toxicity * Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70ml/min/1.73 m\^2 OR a serum creatinine based on age/gender as follows: * =\< 0.6 mg/dL for patients age 1 to \< 2 years * =\< 0.8 mg/dL for patients age 2 to \< 6 years * =\< 1 mg/dL for patients age 6 to 10 2 years * =\< 1.2 mg/dL for patients age 10 to \< 13 years * =\< 1.4 mg/dL for female patients age \>= 13 years * =\< 1.5 mg/dL for male patients age 13 to \< 16 years * =\< 1.7 mg/dL for male patients age \>= 16 years * Bilirubin (sum of conjugated + unconjugated) =\< 1.5 x upper limit of normal (ULN) for age * Serum glutamic pyruvic transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 110 U/L; for the purpose of this study, the ULN for SGPT is 45 U/L * Serum albumin \>= 2 g/dL * Activated partial thromboplastin time (aPTT) and prothrombin time (PT) =\< 1.5 x ULN * All patients and/or their parents or legally authorized representatives must sign a written informed consent; assent, when appropriate, will be obtained according to institutional guidelines * Tissue blocks or slides must be sent per Section 8.5. If tissue blocks or slides are unavailable, the study chair must be notified prior to enrollment. Exclusion Criteria: * Pregnant or breast-feeding women will not be entered on this study; pregnancy tests must be obtained in girls who are post-menarchal; males or females of reproductive potential may not participate unless they have agreed to use an effective contraceptive method * Patients receiving chronic systemic corticosteroids are not eligible * Patients who are currently receiving another investigation drug are not eligible * Patients who are currently receiving other anti-cancer agents are not eligible * Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial * Patients who have known human immunodeficiency virus (HIV), viral hepatitis, or an uncontrolled infection are not eligible * Patients with primary CNS tumors are excluded * Patients with prior history of or known metastatic CNS disease involvement are excluded; (Note: CNS imaging for patients without a known history of CNS disease is only required if clinically indicated) * Patients who have had or are planning to have the following invasive procedures are not eligible: * Major surgical procedure, laparoscopic procedure, open biopsy or significant traumatic injury within 28 days prior to enrollment * Central line placement or subcutaneous port placement is not considered major surgery but must be placed at least 3 days prior to enrollment for external lines (e.g. Hickman or Broviac) and at least 7 days prior to enrollment for subcutaneous port * Core biopsy within 7 days prior to enrollment * Fine needle aspirate within 7 days prior to enrollment * Patients who have received prior solid organ transplantation are not eligible * Patients who in the opinion of the investigator may not be able to comply with the safety monitoring requirements of the study are not eligible * Patients with history of clinically significant bleeding risk (including evidence of active bleeding: intratumoral hemorrhage by current imaging, or bleeding diathesis; bleeding/coagulation disorder; active fracture; non-healing wound; and active gastric ulcer) are not eligible