Pemetrexed or Docetaxel With or Without Erlotinib in Stage IIIB or Stage IV Non-Small Cell Lung Cancer

INCLUSION CRITERIA * Pathologic diagnosis of stage IIIB (with pleural effusion) or IV non-small cell lung cancer * Progression following at least twelve weeks of treatment with single-agent erlotinib (or in combination with other experimental agents) during which time the patients experienced a clinical benefit as assessed by his/her treating physician and corroborated by radiographic assessment (at least one CT scan following at least 4 weeks of erlotinib monotherapy demonstrating stable disease or response on erlotinib therapy). * At least one measurable lesion as defined by modified Response Evaluation Criteria In Solid Tumors (RECIST) criteria * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 * Life expectancy of at least 12 weeks * Absolute neutrophil count (ANC) \>= 1.5x10(9)/L * Platelet count \>= 100x 10(9) * Hemoglobin \>= 8.0 g/dl * Serum creatinine =\< 1.5 upper limit of normal OR calculated creatinine clearance \>= 45 mL/min * Total bilirubin =\< 1.5 x upper limit of normal (ULN) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x ULN * Available baseline diagnostic tumor specimen for correlative studies, any diagnostic material will be acceptable- paraffin block, cell block, fine needle aspirate etc. * Patients must provide verbal and written informed consent to participate in the study * Willingness and ability to comply with scheduled visits, treatment plans, laboratory tests, and other study procedures * Patient must be able to take folic acid, vitamin B12 as well as dexamethasone therapy as per protocol guidelines * Patient must be able to interrupt nonsteroidal anti-inflammatory drugs (NSAIDs) 2 days before (5 days for long-acting NSAIDs), the day of, and 2 days following administration of pemetrexed (this exclusion criteria applies only to patients who have not received pemetrexed chemotherapy prior) EXCLUSION CRITERIA * Active central nervous system disease (CNS) metastases, as indicated by clinical symptoms, cerebral edema or progressive growth (subjects with a clinical history of CNS metastases or cord compression are allowable if they have been definitively treated and are clinically stable for at least 4 weeks before first dose of study treatment for prior whole brain radiation and 2 weeks for prior gamma knife therapy) * More than 1 prior cytotoxic chemotherapy regimen for relapsed or metastatic disease (not including erlotinib) * Any prior epidermal growth factor receptor (EGFR) inhibitor therapy except for erlotinib * Major surgery, chemotherapy, or investigational agents within 3 weeks of treatment day 1 (except for erlotinib). Radiation therapy within 2 weeks of treatment day 1 (except for erlotinib). * Prior treatment with both pemetrexed and docetaxel chemotherapy * Pregnancy or breastfeeding or not receiving adequate contraception (including the patients spouse) * Other severe acute or chronic medical or psychiatric conditions or laboratory abnormality that may increase the risk associated with study participation or study drug administration or may interfere with the interpretation of study results, and in the judgment of the investigator would make the patient inappropriate for entry into this study * Patients who must receive pemetrexed and have the presence of third space fluid which cannot be controlled by drainage * Patients who must receive docetaxel and who have peripheral neuropathy \> grade 2 * Patients who must receive docetaxel and who have had a hypersensitivity reaction to medications formulated with polysorbate 80