Whole-Brain Radiation Therapy or Stereotactic Radiosurgery With or Without Lapatinib Ditosylate in Treating Patients With Brain Metastasis From HER2-Positive Breast Cancer

Inclusion Criteria:

* Pathologically (histologically or cytologically) proven diagnosis of invasive breast cancer
* HER2-overexpressing breast cancer (3+ staining by immunohistochemistry or HER2 gene amplification by fluorescent in situ hybridization \[FISH\] or silver in situ hybridization \[SISH\] \>= 2.0)
* At least 1 measurable unirradiated parenchymal brain metastasis within 21 days prior to study entry; patients who are to undergo SRS must have no more than 10 brain metastases; there is no limit on number of brain metastases for WBRT; the minimum size as measured on T1-weighted gadolinium-enhanced MRI must be as follows according to the number of brain metastases:

  * For a single solitary lesion the size must be \>= 10 mm
  * For 2 or more lesions, the size of at least 2 of the lesions must be \>= 5 mm
  * Patients may also have the following provided the size requirements above are met:

    * Progressive parenchymal brain metastasis following stereotactic radiosurgery for 1-3 brain metastases, with at least 1 new measurable brain lesion
    * Progressive parenchymal brain metastasis following surgical resection of 1-3 brain metastases, with at least 1 measurable brain lesion
* History/physical examination within 21 days prior to study entry
* Karnofsky performance status \>= 60 within 21 days prior to study entry
* Able to swallow and retain oral medication (note: for patients unable to swallow tablets, an oral suspension preparation is acceptable)
* Absolute neutrophil count (ANC) \>= 1,200 cells/mm\^3 (within 21 days prior to study entry)
* Platelets \>= 70,000 cells/mm\^3 (within 21 days prior to study entry)
* Hemoglobin \>= 8.0 g/dL (note: the use of transfusion or other intervention to achieve hemoglobin \[Hgb\] \>= 8.0 g/dL is acceptable) (within 21 days prior to study entry)
* Creatinine \< 1.5 times institutional upper limit of normal (within 21 days prior to study entry)
* Bilirubin \< 1.5 times institutional upper limit of normal (within 21 days prior to study entry)
* Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 3.0 times institutional upper limit of normal with or without liver metastasis (within 21 days prior to study entry)
* Patient must provide study specific informed consent prior to study entry
* Women of childbearing potential must have a negative serum pregnancy test within 21 days prior to study entry
* Sexually active women of childbearing potential and sexually active men must practice adequate contraception during therapy and for 12 months after protocol treatment completion
* Prior lapatinib is allowed as long as the last dose received was \> 21 days prior to study entry and provided the patient has not received it at any time after the diagnosis of brain metastasis

Exclusion Criteria:

* Prior WBRT
* Prior radiation therapy (RT) (any site) with concurrent lapatinib defined as 1 or more days on which the patient received both radiation therapy and lapatinib on the same day
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
* Prior invasive malignancy (except non-melanomatous skin cancer, curatively resected thyroid papillary carcinoma, and invasive and non-invasive cancers related to the breast cancer) unless disease free for a minimum of 3 years
* Leptomeningeal disease
* Prior radiotherapy to the region of the study cancer that would result in overlap of radiation therapy fields except patients who have progressed following stereotactic radiosurgery for 1-3 brain metastases, with at least one new lesion
* Severe, active co-morbidity, defined as follows:

  * Unstable angina and/or congestive heart failure requiring hospitalization within the last 6 months
  * Transmural myocardial infarction within the last 6 months
  * Acute bacterial or fungal infection requiring intravenous antibiotics at the time of study entry
  * Chronic obstructive pulmonary disease exacerbation or other respiratory illness requiring hospitalization or precluding study therapy at the time of study entry
  * Hepatic insufficiency resulting in clinical jaundice and/or coagulation defects; hepatic or biliary disease that is acute or currently active or that requires antiviral therapy (with the exception of patients with Gilbert's syndrome, asymptomatic gallstones, liver metastases, or stable chronic liver disease per investigator assessment)
  * History of left ventricular ejection fraction (LVEF) below institutional normal unless repeated and within institutional normal range within 90 days of study entry
* Grade 2 or greater rash of any cause at time of study entry
* Grade 2 or greater diarrhea of any cause at time of study entry