Docetaxel Plus Lycopene in Castration Resistant, Chemotherapy-Naïve Prostate Cancer Patients

Inclusion Criteria: * Patient must have a histological diagnosis of adenocarcinoma of the prostate and 2 rising pre-study PSA values \>= 1 ng/ml at least 1 week apart within 28 days prior to enrollment * Patients must be unresponsive to androgen-deprivation therapy (ADT), as indicated by a rising PSA level above the ADT nadir * Patient must not have received chemotherapy, biologic therapy, or any other investigational drug for any reason within 28 days prior to start of therapy, and must have recovered from toxicities of prior therapy to grade 1 or less * Patients must have been surgically or medically castrated; if the patient is being treated with medical castration, he must be willing to continue this treatment for the duration of the study; ADT should not be initiated, terminated, or dose-adjusted during the study * Prior external beam radiation therapy (to less than 30% of the bone marrow only) is allowed; at least 28 days must have elapsed since the completion of radiation therapy and the patient must have recovered from side effects; prior treatment with samarium-153 or strontium-86 is allowed if at least eight weeks have elapsed since dosing, and all toxicities have resolved to grade 1; soft tissue disease which has been radiated in the prior 2 months is not assessable as measurable disease * Patients may have received prior surgery; however, at least 21 days must have elapsed since completion of surgery and the patient must have recovered from all side effects * Normal serum bilirubin and serum glutamic oxaloacetic transaminase (SGOT) or serum glutamic pyruvate transaminase (SGPT) =\< 1.5 x the institutional upper limit of normal obtained within 14 days prior to start of therapy; liver function tests should be evaluated prior to each treatment * Serum creatinine =\< 1.5 x the institutional upper limit of normal obtained within 14 days prior to start of therapy * Men of child bearing potential must be willing to consent to using effective contraception while on treatment and for at least 3 months thereafter * Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Absolute neutrophil count \>= 1,500/microliter (mcL) * Hemoglobin of \>= 8.0gm/dL * White blood cell count \> 2,500/mcL * Platelets \>= 100,000/mcL * Patients with lower values may participate if, in the opinion of the investigator, the cytopenias are the result of bone marrow involvement with active prostate cancer * Patients must be able to take oral medications * All patients must be informed and must sign and give written informed consent in accordance with institutional and federal guidelines; patients who are unable to comply with study and/or follow-up procedures are ineligible Exclusion Criteria: * Uncontrolled brain or spinal cord metastases * History of congestive heart failure or myocardial infarction within the previous six months * History of allergy or hypersensitivity to any component of the study drugs * Evidence or history of a bleeding diathesis or coagulopathy, including therapy-induced coagulopathy * Presence of chronic diarrhea (\> grade 1 by Common Toxicity Criteria (CTC)), short bowel syndrome, pancreatic insufficiency, or malabsorption * Presence of any severe or uncontrolled concurrent medical condition which, in the opinion of the investigator, would increase the risk of serious toxicity from the study drugs * Concurrent use of any vitamin, herb, or mineral supplements for at least 14 days prior to start of therapy