A Study to Evaluate Bevacizumab and Chemotherapy or Tarceva in Treating Recurrent or Refractory NSCLC (Non-Small Cell Lung Cancer)

Inclusion Criteria:

* Signed written informed consent
* Histologically or cytologically proven Stage IIIb with pleural effusion, or Stage IV, recurrent non-squamous NSCLC that is recurrent and unresectable
* Progression after one line of platinum-based chemotherapy (patients who have received prior docetaxel treatment are eligible to participate if there are no contraindications for pemetrexed treatment)
* Progression after previous adjuvant chemotherapy, if therapy was completed \>= 6 months prior to randomization and the patient has received one line of therapy for recurrent disease
* (Optional) Availability of archival diagnostic tissue (paraffin tissue block or 2-10 unstained slides representative of the patient's primary cancer)
* ECOG performance status of 0, 1, or 2
* Life expectancy \>= 3 months
* Measurable disease in accordance with RECIST
* Age \>= 18 years
* Use of an acceptable means of contraception (potentially fertile men and women) or documentation of infertility

Exclusion Criteria:

* More than 30 days of prior treatment with an investigational or marketed agent that acts by EGFR inhibition (those with 30 or fewer days on an EGFR inhibitor without disease progression are eligible for enrollment)
* Treatment with an investigational or marketed agent that acts by anti-angiogenic mechanisms
* Previous treatment with more than one platinum-based chemotherapy
* Chemotherapy or radiotherapy within 28 days prior to randomization
* History of hemoptysis (\> 1 teaspoon) or presence of a cavitary lesion
* Clinical history of Grade \> 2 hematemesis within 6 months or Grade 1 hematemesis within 28 days prior to randomization
* History of serious systemic disease, including myocardial infarction within the last 6 months, uncontrolled hypertension (blood pressure \> 150/100 mmHg on medication), unstable angina, New York Heart Association (NYHA) Grade II or greater congestive heart failure, unstable symptomatic arrhythmia requiring medication (patients with chronic atrial arrhythmia, i.e., atrial fibrillation or paroxysmal supraventricular tachycardia are eligible), or Grade II or greater peripheral vascular disease
* History or clinical evidence of CNS or brain metastases or CNS bleeding
* History or clinical evidence of hemorrhagic or thrombotic stroke within the 6 months prior to randomization
* Centrally located lesions and lesions that abut major blood vessels
* Ongoing treatment with full-dose warfarin (or its equivalent) or heparin (or its equivalent; e.g., Lovenox(R))
* In-patient surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to randomization
* Minor surgical procedure, fine needle aspirations, or core biopsy within 7 days prior to randomization
* Anticipation of need for a major surgical procedure during the course of the study
* Serious, non-healing wound, ulcer, or bone fracture
* Inability to take oral medication or requirement for IV alimentation or total parenteral nutrition with lipids, or prior surgical procedures affecting absorption
* Any of the following abnormal hematologic values (within 1 week prior to randomization): ANC \<= 1,500 cells/uL; platelet count \<= 100,000 cells/uL; Hemoglobin \<= 9.0 g/dL; International normalized ratio (INR) \&gt; 1.5 x upper limit of normal (ULN)
* For patients who will receive docetaxel, any of the following abnormal liver function tests (within 1 week prior to randomization): Serum bilirubin greater than ULN; Albumin \<= 2.5 g/dL; Serum ALT \>= 1.5 x ULN; Serum AST \>= 1.5 x ULN; Alkaline phosphatase \>= 2.5 x ULN
* Other baseline laboratory values: Serum creatinine \&gt; 2.0 x ULN; Uncontrolled hypercalcemia ( \&gt; 11.5 mg/dL); Urinary protein/creatinine ratio \>= 1 (spot urine) or clinically significant impairment of renal function; Estimated creatinine clearance \&lt; 45 mL/min (for patients who will receive pemetrexed)
* Any active systemic bacterial, fungal, or viral infection, including known hepatitis C and HIV
* Pregnant or breast-feeding
* Presence of another cancer within 5 years prior to randomization, except for adequately treated carcinoma in situ of the cervix or non-melanomatous skin cancer
* Evidence of confusion or disorientation, or history of major psychiatric illness that may impair the patient's understanding of the Informed Consent Form