Study of Vintafolide (MK-8109, EC145) in Participants With Progressive Adenocarcinoma of the Lung (MK-8109-008, EC-FV-03)

Inclusion Criteria: * Advanced, progressive, adenocarcinoma of the lung. * Previously received at least 2 cytotoxic containing chemotherapeutic regimens (can include an epidermal growth factor receptor \[EGFR\] inhibitor). There is no upper limit to the number of prior chemotherapeutic regimens. * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2. * At least 4 weeks from prior therapy and recovered from associated acute toxicities. * Radiographic evidence of measurable disease and ertafolide "positive" tumor. * Adequate bone marrow reserve, hepatic, and renal function. * Negative serum pregnancy test for women of childbearing potential and willingness to practice contraceptive methods. Exclusion Criteria: * Serious comorbidities (as determined by the Principal Investigator). * History of carcinomatous peritonitis. * History of severe bowel obstruction (as determined by the Principal Investigator). * Women who are pregnant or lactating. * Prior radiation therapy to assessable disease, unless disease progression is confirmed at that site. * Participants requiring palliative radiotherapy at time of study entry. Note: Participants with central nervous system (CNS) metastasis are eligible if a) they have been treated for the CNS metastasis and have been clinically stable (with regard to their CNS disease) for \>4 weeks and b) they do not require steroids or antiseizure medications (i.e., for seizure control), or if the CNS metastasis has been untreated to date, it is not associated with a midline shift or significant edema and there is no clinically-evident requirement for steroids or antiseizure medication. In either situation, participants must be off steroids and/or antiseizure medications for at least 14 days.