Sublingual Anvirzel in Advance Non-Small Cell Lung Cancer (NSCLC)

Study Drug Administration: If you are eligible and agree to take part in the study, you will be assigned to a dose level of nerium oleander based on when you join this study. Up to 5 dose levels of nerium oleander will be tested. At least 3 participants will be enrolled at each dose level. The first group of participants will receive the lowest dose level. Each new group will receive a higher dose than the group before it, if no intolerable side effects were seen. This will continue until the highest tolerable dose of nerium oleander is found. You will take nerium oleander by mouth by placing it under your tongue. You should hold the nerium oleander under your tongue for 3 minutes before swallowing. It is very important for you to hold the nerium oleander under your tongue for 3 full minutes. Holding it under your tongue for 3 minutes before swallowing helps your body to take in the highest amount of the drug that you can receive. If you hold the nerium oleander under your tongue for less than 3 minutes, your body will not receive as much of the study drug and may not possibly benefit as much. You will take nerium oleander 3 times a day while participating in this study. Nerium oleander should be taken on an empty stomach or at least 15 minutes before any large meal, to help your body take in as much of the drug as possible. Study Visits: Each of your chemotherapy cycles are 21 days. Each week while on study, you will complete the questionnaire about any symptoms you may be having. It should take about 5 minutes to complete it each time. Cycle 1: On Day -7 (7 days before you start chemotherapy): * You will complete the questionnaire about your physical and mental health. It should take about 5 minutes to complete it. * Blood (about 2 teaspoons each time) will be drawn 6 times over 8 hours for pharmacokinetic (PK) testing. PK testing measures the amount of study drug in the body at different time points. * Blood (about 6 teaspoons) will be drawn to learn if the study drug is reducing inflammation. * Blood (about 2 teaspoons) will be drawn to test the effect of the study drug on your immune system. On Day -6, blood (about 2 teaspoons each time) will be drawn 1 time for PK testing. On Day 1 (the day you start chemotherapy): * You will be asked about any symptoms you may be having or drugs you may be taking. * You will have a physical exam, including measurement of weight and vital signs. * Your performance status will be recorded. * You will complete the questionnaire about your physical and mental health. * Blood (about 1 teaspoon) will be drawn for routine tests. * Blood (about 2 teaspoons each time) will be drawn 6 times over 8 hours for PK testing. * Blood (about 6 teaspoons) will be drawn to learn if the study drug is reducing inflammation. * Blood (about 2 teaspoons) will be drawn to test the effect of the study drug on your immune system. * You will have an EKG. On Day 2: * Blood (about 2 teaspoons) will be drawn for PK testing. * Blood (about 6 teaspoons) will be drawn to learn if the study drug is reducing inflammation. * Blood (about 2 teaspoons) will be drawn to test the effect of the study drug on your immune system. On Day 8 (+/- 2 days): * Blood (about 6 teaspoons) will be drawn to learn if the study drug is reducing inflammation. * Blood (about 2 teaspoons) will be drawn to test the effect of the study drug on your immune system. On Day 1 of Cycles 2-3: * You will be asked about any symptoms you may be having or drugs you may be taking. * You will have a physical exam, including measurement of weight and vital signs. * Blood (about 1 teaspoon) will be drawn for routine tests. * Your performance status will be recorded. * You will have an EKG. * You will complete the questionnaire about your physical and mental health. * On Day 1 of Cycle 3 only, you will have a CT scan to check the status of the disease. On Day 1 of Cycle 4: * You will be asked about any symptoms you may be having or drugs you may be taking. * You will have a physical exam, including measurement of weight and vital signs. * You will complete the questionnaire about your physical and mental health. * Blood (about 1 teaspoon) will be drawn for routine tests. * Your performance status will be recorded. * You will have an EKG. * Blood (about 2 teaspoons each time) will be drawn 6 times over 8 hours for PK testing. * Blood (about 6 teaspoons) will be drawn to learn if the study drug is reducing inflammation. * Blood (about 2 teaspoons) will be drawn to test the effect of the study drug on your immune system. On Day 2 of Cycle 4: * Blood (about 2 teaspoons) will be drawn for PK testing. On Day 8 and Day 21 of Cycle 4 (+/- 2 days): * Blood (about 6 teaspoons) will be drawn to learn if the study drug is reducing inflammation. * Blood (about 2 teaspoons) will be drawn to test the effect of the study drug on your immune system. Length of Study: You may continue taking the study drug for as long as the doctor thinks it is in your best interest or up to 4 cycles. You will no longer be able to take the study drug if the disease gets worse, if intolerable side effects occur, or if you are unable to follow study directions. Your participation on the study will be over after the follow-up visit. End-of-Dosing Visit: After your last dose of study drug, you will return to the clinic. The following tests and procedures will be performed: * You will be asked about any symptoms you may be having or drugs you may be taking. * You will have a physical exam, including measurement of weight and vital signs. * Blood (about 1 teaspoon) will be drawn for routine tests. * You will have an EKG. * You will have a CT scan to check the status of the disease. * You will complete both questionnaires. Follow-Up Visit: About 30 days after your last dose of study drug, the following tests and procedures will be performed: * You will be asked about any symptoms you may be having or drugs you may be taking. * You will have a physical exam, including measurement of weight and vital signs. * Blood (about 1 teaspoon) will be drawn for routine tests. * You will have an EKG. * You will complete both questionnaires. This is an investigational study. Nerium oleander is not FDA approved or commercially available. Its use in this study is considered investigational. Up to 36 participants will be enrolled in this study. All will take part at MD Anderson.