Pemetrexed Disodium With or Without Erlotinib Hydrochloride in Treating Patients With Stage IIIB-IV or Recurrent Non-Small Cell Lung Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed advanced (stage IIIB with a malignant pleural effusion or stage IV disease) or recurrent nonsquamous NSCLC * Patients must have at least one measurable disease per RECIST criteria; all sites of disease must be assessed within 4 weeks prior to registration * Patient must have disease progression after one prior combinational chemotherapy and/or targeted therapy other than pemetrexed or an epidermal growth factor receptor (EGFR) ) tyrosine kinase inhibitor (TKI) (such as erlotinib, gefitinib, or a second generation EGFR TKI); prior monoclonal antibody against EGFR is allowed) for metastatic disease, or relapse while receiving adjuvant therapy, or within 12 months of completing adjuvant therapy * All patients will be screened for brain metastasis within 6 weeks prior to registration; patients with treated and stable brain metastases must have been treated with surgery and/or radiation and are asymptomatic and are no longer taking corticosteroids * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 or Karnofsky \>= 60% * Absolute neutrophil count \>= 1,500/uL * Hemoglobin \>= 8.0 g/dL * Platelets \>= 100,000/uL * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN), except in known hepatic metastasis, wherein may be =\< 3.0 X ULN * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3.0 x institutional ULN, except in known hepatic metastasis, wherein may be =\< 5.0 X ULN * Creatinine clearance \>= 45 mL/min for patients with creatinine levels above institutional normal * Patients must not be pregnant or breastfeeding since there is no information regarding the use of these agents in this population; a negative serum or urine pregnancy test is required within 14 days prior to registration if pre- or perimenopausal (i.e., last menstrual period within one year of registration); both pemetrexed and erlotinib are Class D agent with the potential for teratogenic or abortifacient effects; patients both females and males with reproductive potential (i.e. menopausal for less than 1 year and not surgically sterilized) must practice contraceptive measures throughout the study * Patients taking Warfarin or nonsteroidal anti-inflammatory drugs (NSAIDs) are eligible; patients with mild to moderate renal insufficiency should avoid taking NSAIDs with short elimination half-lives for a period of 2 days before, the day of, and 2 days following administration of Alimta; if the patient is taking other cytochrome P450 3A4 (CYP3A4) inducers or inhibitors, they must be discontinued at least one week prior to starting erlotinib * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had immunotherapy, hormone, chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Patients who have received pemetrexed or an EGFR TKI (such as erlotinib, gefitinib, or a second generation anti-EGFR TKI) for their metastatic disease should be excluded from this clinical trial; other molecularly targeted agent, including monoclonal antibody or vaccine against EGFR or angiogenesis inhibitor, is allowed * Patients may not be receiving any other investigational or commercial agents or therapies other than those described below with the intent to treat the patient's malignancy * Patients with uncontrolled brain metastases should be excluded from this clinical trial because of their poor prognosis * History of allergic reactions attributed to compounds of similar chemical or biologic composition to erlotinib or pemetrexed or other agents used in the study * Patients with gastrointestinal tract disease resulting in an inability to take oral medication or a requirement for IV alimentation, prior surgical procedures affecting absorption, or active peptic ulcer disease, are ineligible * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection (such as bacteremia or active hepatitis), symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Patients with immune deficiency are at increased risk of lethal infections when treated with marrow-suppressive therapy; therefore, human immunodeficiency virus (HIV)-positive patients receiving combination anti-retroviral therapy are excluded from the study because of possible pharmacokinetic interactions with erlotinib or pemetrexed or other agents administered during the study; appropriate studies will be undertake in patients receiving combination anti-retroviral therapy when indicated