Topotecan Hydrochloride and Doxorubicin Hydrochloride in Treating Relapsed or Refractory Small Cell Lung Cancer

Inclusion Criteria: * Pathologically proven diagnosis of small cell lung cancer (SCLC) * Have received at least one prior chemotherapy regimen for SCLC * Primarily refractory or relapsed disease * Measurable or evaluable disease: measurable disease in 2 dimensions on imaging studies performed within 4 weeks of starting treatment * Greater than 2 weeks since last treatment (chemotherapy or radiation) provided subject has recovered from side effects of treatment prior to the study * Karnofsky score \>= 70; (Eastern Cooperative Oncology Group \[ECOG\] 0-2) * No active secondary malignancy; patients with other prior malignancies will be included, provided they have been disease-free for at least five years * Patients with adequately treated basal cell or squamous cell carcinoma of the skin, adequately treated non-invasive carcinomas will be eligible * White blood cell (WBC) count \>= 3,500/mm\^3 within 7 days prior to starting treatment, OR * Absolute neutrophil count (ANC) \>= 1,500/ul within 7 days prior to starting treatment * Platelet count \>= 100,000/mm\^3 within 7 days prior to starting treatment * Serum creatinine less than 1.5 times the upper limits of normal within 7 days prior to starting treatment * Serum aspartate aminotransferase (AST) and alanine aminotransferase (ALT) less than 1.5 times the upper limits of normal within 7 days prior to starting treatment in the absence of liver metastasis; in the presence of liver metastasis serum AST and ALT less than or equal to 5.0 times the upper limits of normal within 7 days prior to starting treatment * Serum alkaline phosphatase less than 2.5 times the upper limits of normal within 7 days prior to starting treatment in the absence of liver metastasis; in the presence of liver metastasis serum alkaline phosphatase less than or equal to 5.0 times the upper limits of normal within 7 days prior to starting treatment * Women of child-bearing potential must have a negative pregnancy test within 7 days of initiating study; (no childbearing potential is defined as age 55 years or older and no menses for two years or any age with surgical removal of the uterus and/or both ovaries) * Non-pregnant and non-nursing; men and women of reproductive potential may not participate unless they have agreed to use an effective contraceptive method while on the study * Able to return for treatment and follow-up as specified in the protocol * Able to give informed consent Exclusion Criteria: * Known hypersensitivity to any component of topotecan or doxorubicin or other required drugs in the study * Any co morbidity or condition which, in the opinion of the investigator, may interfere with the assessments and procedures of this protocol * Ejection fraction below the lower limit of normal (\< 50%) * Uncontrolled intercurrent illnesses including, but not limited to unstable angina or uncontrolled cardiac arrhythmia, chronic liver disease, complete left bundle branch block, obligate use of a cardiac pacemaker, ST depression of \> 1 mm in two or more leads and/or T wave inversions in two or more contiguous leads, congenital long QT syndrome, history of or presence of significant ventricular or atrial tachyarrhythmias, clinically significant resting bradycardia (\< 50 beats per minute), corrected QT (QTc) \> 480 ms on screening electrocardiogram that could jeopardize the patient?s ability to receive the chemotherapy described in the protocol safely * Women who are pregnant (confirmed by a serum pregnancy test in females of reproductive potential) or breast-feeding; women of child-bearing potential and sexually active males must be advised to take precautions to prevent pregnancy during treatment (unless the subject or subject?s partner(s) is sterile (i.e. women who have had a hysterectomy or have been post-menopausal for at least twelve consecutive months) or remain abstinent, men and women of reproductive potential must agree to use TWO of the following forms of birth control every time they have sex throughout the study and for up to 3 months following discontinuation of study drug: condoms (male or female) with or without a spermicidal agent, diaphragm or cervical cap with spermicidal, intrauterine device (IUD), or surgical sterilization while participating in this study; hormonal birth control methods are not permitted * Inability to co-operate with the requirements of the protocol