Erlotinib in Treating Patients With Advanced Non-Small Cell Lung Cancer, Ovarian Cancer, or Squamous Cell Carcinoma of the Head and Neck

Inclusion Criteria:

* Patients must have histologically or cytologically confirmed metastatic or unresectable non-small cell lung cancer, squamous cell carcinoma of the head and neck, or ovarian cancer
* Eligible patients must have been off previous anticancer therapy including chemotherapy, radiotherapy, biological therapy, or other investigational therapy for at least 4 weeks before study entry (6 weeks if prior therapy included nitrosoureas or mitomycin C)
* ECOG performance status =\< 2 (Karnofsky \>= 60%)
* Life expectancy of greater than 12 weeks
* Leukocytes \>= 3,000/ul
* Absolute neutrophil count \>= 1,500/ul
* Platelets \>= 100,000/ul
* Total bilirubin within normal institutional limits
* Creatinine within normal institutional limits OR creatinine clearance \> 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal
* Patients must have measurable or assessable disease
* The effects of OSI-774 on the developing human fetus are unknown; for this reason women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately
* Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

* Patients who have had 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 with prior treatment with small molecule inhibitors of EGFR, including erlotinib and gefitinib, are not eligible for this study
* Patients may not be receiving any other investigational agents
* Patients with uncontrolled brain metastasis; patients with brain metastases must have stable neurologic status following local therapy (surgery or radiation) for at least 4 weeks, and must be without neurologic dysfunction that would confound the evaluation of neurologic and other adverse events
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to OSI-774
* 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
* Pregnant women are excluded from this study because OSI-774 is an agent with the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with OSI-774, breastfeeding should be discontinued if the mother is treated with either agent
* HIV-positive patients receiving combination anti-retroviral therapy are excluded from the study because of possible pharmacokinetic interactions with OSI-774 or other agents administered during the study; appropriate studies will be undertaken in patients receiving combination anti-retroviral therapy when indicated
* Patients with significant ophthalmologic abnormalities, including: severe dry eye syndrome, kerato-conjunctivitis sicca, Sjogren's syndrome, severe exposure keratopathy, disorders that might increase the risk for epithelium-related complications (e.g. bullous keratopathy, aniridia, severe chemical burns, neutrophilic keratitis); patients with mild forms of any of the above, an asymptomatic history, or a normal ophthalmologic examination may be considered for inclusion at the discretion of the investigator; an ophthalmologic exam is not needed prior to this study unless clinically indicated; patients with treatable conditions (e.g. infectious keratitis/conjunctivitis, allergic conjunctivitis) may be reevaluated for study eligibility after treatment or resolution of the condition; use of contact lenses during the course of this trial may increase the risk of corneal complications and will be strongly discouraged
* Serious, non-healing wound ulcer, or bone fracture
* Major surgical procedure, open biopsy or significant traumatic injury within 14 days prior to Day 1; following such procedures or injuries, wound healing should be evident prior to initiation of therapy