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 neutr…