Pemetrexed Disodium or Erlotinib Hydrochloride as Second-Line Therapy in Treating Patients With Advanced Non-small Cell Lung Cancer

Inclusion Criteria: * Documented recurrence or disease progression of NSCLC * NSCLC must be confirmed by pathologic examination, either on initial diagnosis or disease recurrence/progression; mixed histology allowed if all components consistent with NSCLC * Measurable disease, defined as at least one lesion whose longest diameter can be accurately measured as \>= 2.0 cm by conventional techniques or as \>= 1.0 cm by spiral computed tomography (CT); if spiral CT is used, it must be used for both pre- and post- treatment tumor assessments * Prior radiation therapy is permitted as long as: * Recovered from the toxic effects of radiation treatment before study entry, except for alopecia * =\< 25% of bone marrow radiated * Presence of measurable disease whether in-field disease progression/recurrence or disease outside the treatment fields of radiation port * Absolute neutrophil count (ANC) \>= 1,500 uL * Platelet (PLT) \>= 100,000 uL * Hemoglobin (Hgb) \>= 10 g/dL * Total bilirubin: within normal institutional limits (WNL) OR direct bilirubin =\< upper limit of normal (ULN) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x ULN * International normalized ratio (INR) =\< 1.5 * Calculated creatinine clearance \>= 45 mL/min using the Cockcroft-Gault formula * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, or 2 * Negative pregnancy test done =\< 7 days prior to pre-registration, for women of childbearing potential only * Ability to provide informed consent * Life expectancy \>= 12 weeks * Tissue available and willing to submit tissue for central pathology review and EGFR evaluation; performed on original diagnostic/recurrent tissue (preferably paraffin-embedded tissue blocks); if institution unable to release tissue blocks, willing to submit 25 unstained slides (15 sections cut at 5 microns mounted on charged slides and 10 sections cut at 10 microns mounted on uncharged slides) * Must be previously treated for advanced disease with only 1 chemotherapy regimen which must contain cytotoxic agent(s); adjuvant/neoadjuvant treatment with cytotoxic agent(s) administered \< 12 months (from date chemotherapy was started) prior to pre-registration will be considered as one prior treatment; NOTE: adjuvant/neoadjuvant treatment administered \>= 12 months, use of targeted agents such as monoclonal antibodies prior to pre-registration will NOT be counted as one prior treatment; patient could have had adjuvant/neoadjuvant chemotherapy \>= 12 months and 1 systemic chemotherapy regimen for metastatic or recurrent disease * Able to take folic acid, vitamin B12 supplementation, and dexamethasone * Able to permanently discontinue aspirin dose of \>= 1.3 grams/day \>= 10 days before and after pemetrexed treatment * Fertile patients must use effective contraception * Able to take folic acid, vitamin B\_12 supplementation, and dexamethasone * Stable brain metastasis that have been treated with either whole brain radiation therapy or gamma knife surgery and are off steroid treatment for \> 14 days prior to pre-registration, if applicable * Willingness to return to enrolling institution for treatment and follow-up Exclusion Criteria: * Any of the following: * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception * Any clinically significant infection, at the treating physician's discretion * Known human immunodeficiency virus (HIV) positive patients * Impairment of gastrointestinal (GI) function, inability to swallow pills in the absence of a feeding tube, or GI disease that may significantly alter absorption of oral medications (e.g. ulcerative disease, uncontrolled nausea and vomiting, malabsorption syndromes, bowel obstruction, etc) * Serious condition that, in the opinion of the investigator, would compromise the patient's ability to complete the study or increase the risk for serious adverse events * Any of the following prior therapies: * Prior radiation to \> 25% of bone marrow * EGFR tyrosine kinase inhibitors * Pemetrexed * Chemotherapy =\< 3 weeks prior to pre-registration * Mitomycin C/nitrosoureas =\< 6 weeks prior to pre-registration * Immunotherapy =\< 2 weeks prior to pre-registration * Biologic therapy =\< 2 weeks prior to pre-registration * Gene therapy =\< 2 weeks prior to pre-registration * Full field radiation therapy =\< 4 weeks prior to pre-registration * Limited field radiation therapy =\< 2 weeks prior to pre-registration * Major surgery (i.e., laparotomy), open biopsy, or significant traumatic injury =\< 4 weeks prior to pre-registration or anticipation of need for major surgical procedure during the course of the study; minor surgery =\< 2 weeks prior to pre-registration; insertion of a vascular access device is not considered major or minor surgery in this regard * Other chemotherapy, immunotherapy, hormonal therapy, radiotherapy, or any ancillary therapy considered investigational (utilized for a non-Food and Drug Administration \[FDA\]-approved indication and in the context of a research investigation) =\< 4 weeks prior to pre-registration * Steroid therapy for brain metastasis =\< 14 days prior to pre-registration * Symptomatic serosal effusion (\>= Common Terminology Criteria for Adverse Events \[CTCAE\] v3.0 grade 2 dyspnea) that is not amenable to drainage prior to pre-registration * Other invasive solid or hematologic malignancy; exceptions: prior malignancy was diagnosed and definitively treated \>= 5 years previously with no subsequent evidence of recurrence; patients with a history of low-grade (Gleason score =\< 6) localized prostate cancer will be eligible even if diagnosed \< 3 years prior to pre-registration; these patients may continue on medications concomitantly to maintain their disease remission as necessary; patients with carcinoma in situ, regardless of organ involvement, or non-melanoma cutaneous carcinomas are eligible if these were definitively treated \>= 3 years previously with no subsequent evidence of recurrence; Note: patients with breast cancer that was definitively treated \> 5 years earlier but continue to receive aromatase inhibitors are NOT eligible * Only non-measurable disease, defined as all other lesions, including small lesions whose longest diameter measures \< 2 cm with conventional techniques or \< 1.0 cm with spiral CT, and truly non-measurable lesions, which include the following as per Response Evaluation Criteria In Solid Tumors (RECIST) criteria dated June 1999: * Bone lesions * Leptomeningeal disease * Ascites * Pleural/pericardial effusion * Inflammatory breast disease * Lymphangitis cutis/pulmonis * Abdominal masses that are not confirmed and followed by imaging techniques * Cystic lesions * Single disease site in prior radiation field * Any of the following concurrent severe and/or uncontrolled medical conditions: * Angina pectoris * History of congestive heart failure =\< 3 months prior to pre-registration, unless ejection fraction \> 40% * Myocardial infarction =\< 6 months prior to pre-registration * Cardiac arrhythmia * Diabetes mellitus * Hypertension * Any other severe underlying diseases which are, in the judgment of the investigator, inappropriate for entry into this study * Respiratory symptoms \> CTCAE grade 1