The goal of this clinical research study is to find the highest tolerable dose of vemurafenib that can be given in combination with carboplatin and paclitaxel patients with advanced cancer. The safety of the study drug combination will also be studied.

Vemurafenib is designed to block a protein (called mutated BRAF) that is only found in moles (spots) of the skin and certain types of cancer cells. This drug may slow the growth of or kill these cells.

Carboplatin is designed to slow the growth of cancer cells by stopping them from making new DNA (the genetic material of cells).

Paclitaxel is designed to slow the growth of cancer cells by stopping them from dividing into new cells.

Study Groups:

If you are found to be eligible and decide to take part, you will be assigned to a study group based on when you join this study. Up to 8 groups of 3-6 participants will be enrolled in this study.

The dose of vemurafenib and the doses of carboplatin and paclitaxel you receive will depend on when you joined this study. The first group of participants will receive the lowest dose level of vemurafenib, carboplatin, and paclitaxel. Each new group will receive a higher dose level of the study drug combination than the group before it, if no intolerable side effects were seen. This will continue until the highest tolerable dose of the combination is found. After that, 10 additional participants will be enrolled.

Study Drug Administration:

Each study cycle is 3 weeks.

You will start taking paclitaxel and carboplatin on Day 1 of Cycle 1. Paclitaxel will be given by vein over 3 hours, and carboplatin will be given by vein over 30-60 minutes. You may be given medications to reduce the risk of nausea and allergic reaction before these study drugs are given. Both paclitaxel and carboplatin will be given every 3 weeks.

You will start taking vemurafenib by mouth in the evening on Day 1 of Cycle 1. You will then take vemurafenib twice a day, every day starting with Day 2 of Cycle 1.

Study Visits:

At every study visit, you will be asked about any drugs you may be taking, how you are feeling, and if you have had any side effects.

On Day 1 of Cycle 1:

• You will have a physical exam, including measurement of your weight and vital signs if not done in the past 8 days.
• Your performance status will be recorded.
• Blood (about 1 tablespoon) will be drawn for routine tests if this was not done in the past 10 days.

On Day 8 of Cycle 1:

• You will have a physical exam, including measurement of your vital signs.
• Your performance status will be recorded.
• Blood (about 1 tablespoon) will be drawn for routine tests.

On Day 1 of Cycles 2 and beyond:

• You will have a physical exam, including measurement of your weight and vital signs.
• Your performance status will be recorded.
• Blood (about 1 tablespoon) will be drawn for routine tests.
• In Cycle 2 only, you will have an ECG.

After Cycle 4, if you are tolerating the study drug combination well and the study doctor agrees, you may have your Day 1 visit every other cycle.

Every 6 weeks (every 2 cycles), you will have a CT scan, MRI scan, bone scan, and/or x-ray to check the status of the disease.

Length of Study Participation:

You may continue taking the study drug combination for as long as the doctor thinks it is in your best interest.

You will no longer be able to take the study drugs if the disease gets worse, if you start having other health problems, if intolerable side effects occur, or if you are unable to follow study directions.

Your participation on the study will be over when you have completed the End-of-Study Visit.

End-of-Study Visit:

Within 4 weeks after your last dose of study drugs:

• You will have a physical exam, including measurement of your weight and vital signs.
• Your performance status will be recorded.
• Blood (about 1 tablespoon) will be drawn for routine tests.
• You will have an ECG.
• You will have a CT scan, MRI scan, bone scan, and/or x-ray to check the status of the disease.

This is an investigational study. Vemurafenib is FDA approved and commercially available to treat advanced melanoma with mutated BRAF. Carboplatin and paclitaxel are FDA approved for certain types of cancers, including lung and ovarian cancers. Using the study drug combination to treat advanced cancer with a BRAF mutation is considered investigational.

Up to 96 participants will be enrolled in this study. All will take part at MD Anderson.

Inclusion Criteria:

1. Patient must be age >/= 12 years.
2. Patient must have histologically or cytologically confirmed diagnosis of advanced solid tumor or lymphoma harboring a BRAF mutation, for which no standard therapy is available, is resistant/refractory to standard therapy, has relapsed after standard therapy, or has no standard therapy that improves survival by at least three months.
3. Patient with QTc interval must be less than 500 msec.
4. Patient must have completed any prior cytotoxic chemotherapy or radiation therapy at least 21 days prior to starting the study drug(s), except selective RAF inhibitors (vemurafenib, dabrafenib or LGX818). There is no washout period for prior selective RAF inhibitors. Patients must be at least 5 half-lives or 3 weeks, whichever is shorter, from their previous targeted or biologic therapy. Local palliative radiation therapy that is not delivered to all target lesions is allowed immediately before or during treatment.
5. Patients must have evaluable disease for response.
6. Patient must have an ECOG performance status of 0 to 2.
7. Patient must have adequate liver and renal function as documented by the following laboratory test results within 14 days prior to starting therapy: total bilirubin less than or equal to 2 x upper limit of normal (ULN) (exceptions may apply to benign non-malignant indirect hyperbilirubinemia such as Gilbert syndrome); AST (SGOT) and ALT (SGPT) less than or equal to 2.5 X ULN or less than or equal to 5 X ULN if liver metastasis is present; serum creatinine less than or equal to 2 X ULN
8. Patient must have adequate bone marrow function as documented by the following laboratory test results within 14 days prior to starting therapy: platelets greater than 75,000/mm^3;absolute neutrophil count (ANC) greater than 1000/mm^3; hemoglobin greater than 8.0 g/dL
9. Patient (man or woman) must agree to practice effective contraception during the entire study period, unless documentation of infertility exists, and for at least 4 weeks after the last dose of the study drug(s).
10. Patient must be willing and able to sign the informed consent form.

Exclusion Criteria:

1. Patients with clinically significant illnesses which could compromise participation in the study, including, but not limited to: active or uncontrolled infection; or unstable angina pectoris, myocardial infarction within the past 6 months, or uncontrolled cardiac arrhythmia.
2. Patients with an inability to swallow tablets or capsules
3. Patients with leptomeningeal disease;
4. Patients who are pregnant or breastfeeding