Vaccine Therapy, Chemotherapy, and Radiation Therapy in Treating Patients With Stage III Non-Small Cell Lung Cancer That Cannot Be Removed With Surgery

DISEASE CHARACTERISTICS: * Histologically confirmed non-small cell lung cancer * Stage III (locally advanced) disease * Unresectable disease * Carcinoembryonic antigen (CEA)-positive (staining ≥ 20% of cells) tumor by immunohistochemistry * HLA-A2-positive * No distant metastases PATIENT CHARACTERISTICS: Age * 18 and over Performance status * ECOG 0-1 Life expectancy * At least 6 months Hematopoietic * Granulocyte count ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 * Absolute lymphocyte count ≥ 600/mm\^3 * Hemoglobin ≥ 10 g/dL Hepatic * Bilirubin \< 1.5 mg/dL * AST ≤ 2 times upper limit of normal * Hepatitis B and C negative Renal * Creatinine normal OR * Creatinine clearance \> 60 mL/min Cardiovascular * No unstable or newly diagnosed angina pectoris * No myocardial infarction within the past 6 months * No New York Heart Association class II-IV congestive heart failure Immunologic * HIV negative * No altered immune function * No active or history of eczema * No atopic dermatitis * No autoimmune disease, including any of the following: * Autoimmune neutropenia, thrombocytopenia, or hemolytic anemia * Systemic lupus erythematosus * Sjögren's syndrome * Scleroderma * Myasthenia gravis * Goodpasture's syndrome * Addison's disease * Hashimoto's thyroiditis * Active Graves' disease * Multiple sclerosis * No known history of allergy or serious reaction to prior vaccination with vaccina * No known allergy to eggs * No active or history of extensive psoriasis, severe acneiform rash, impetigo, varicella zoster, burns, or other traumatic or pruritic skin condition Other * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for 4 months after study participation * No history of seizures or encephalitis * Able to avoid close household contact with the following individuals for at least 3 weeks after vaccinia vaccination: * Children under 3 years of age * Pregnant or nursing women * Individuals with a history of or active eczema or other eczematoid skin disorders * Individuals with other acute, chronic, or exfoliative skin conditions (e.g., atopic dermatitis, impetigo, burns, varicella zoster, severe acne, or other open rashes or wounds) * Immunodeficient or immunosuppressed individuals, including HIV-positive persons, by disease or therapy * No other active malignancy within the past 2 years * No other concurrent serious illness PRIOR CONCURRENT THERAPY: Biologic therapy * At least 3 years since prior immunotherapy with related vaccinia and fowlpox vaccines * At least 3 years since prior antigen-specific peptides * No other concurrent immunotherapy Chemotherapy * No prior paclitaxel or carboplatin for lung cancer * At least 3 years since prior chemotherapy * No other concurrent chemotherapy Endocrine therapy * No concurrent steroids, except for any of the following: * Topical steroids * Inhaled steroids for mild or moderate asthma * Dexamethasone as premedication for paclitaxel OR for short-term doses (48-72 hours in duration) to control refractory nausea that is not responding to other antiemetics * Systemic corticosteroids for ≥ grade 3 radiation pneumonitis * No steroid eye-drops for at least 3 weeks after vaccinia vaccination * No concurrent hormonal therapy * No concurrent systemic glucocorticoids Radiotherapy * No prior radiotherapy to the lung fields * No prior thoracic radiotherapy for lung cancer * No other concurrent radiotherapy Surgery * Surgical scars must be healed * No prior splenectomy * No concurrent major surgical procedure Other * Recovered from all prior therapy * No other concurrent anticancer agent or therapy