Different people have different biomarkers (chemical "markers" in the blood that may be related to your reaction to study drugs). If researchers know about your biomarkers before you receive treatment, they may be able to prescribe a treatment that is better suited to your body's specific needs.

The goal of this clinical research study is to learn if drug or drug combinations based on your biomarkers can help to control NSCLC. The safety of these drug combinations will also be studied.

The Study Drugs:

Erlotinib hydrochloride, MK-2206, AZD6244, and Sorafenib are targeted therapies. Targeted therapy is a type of drug that blocks the growth of cancer cells by interfering with specific targeted molecules needed for tumor growth, rather than by simply interfering with rapidly dividing cells (for example with traditional chemotherapy).

Study Groups:

If you are found to be eligible to take part in this study, you will be assigned to 1 of 4 groups:

• If you are in Group 1, you will take erlotinib alone.
• If you are in Group 2, you will take erlotinib and MK-2206.
• If you are in Group 3, you will take AZD6244 and MK-2206.
• If you are in Group 4, you will take sorafenib alone.

The group you are in will be assigned by a computer. The results of your screening tests will be used to determine (and may limit) which of the 4 groups you may be eligible to be assigned to. Your likelihood of being in any 1 group over another may also be affected by how well that treatment has done in earlier study participants. Your study doctor will tell you which group you have been assigned.

Study Drug Administration:

Each cycle is 28 days.

• If you are in Group 1, you will take erlotinib hydrochloride by mouth 1 time every day.
• If you are in Group 2, you will take MK-2206 by mouth 1 time every week. You will take erlotinib hydrochloride by mouth 1 time every day.
• If you are in Group 3, you will take MK-2206 by mouth 1 time per week. You will take AZD6244 by mouth 1 time every day.
• If you are in Group 4, you will take sorafenib by mouth 2 times every day.

If you will take erlotinib hydrochloride (Groups 1 and 2), you should take the tablets in the morning. You should take the drug 1 hour before or 2 hours after a meal, with no more than 7 ounces of water. If you forget to take a dose, the last missed dose should be taken as soon as you remember, as long as it is at least 12 hours before the next dose. The next day, you should take the scheduled dose at the usual time. You should try not to vomit for at least 30 minutes after taking the drug. If you feel nauseated before or after taking the erlotinib, you should take an anti-nausea drug. You may take an extra dose of erlotinib if you vomit within 30 minutes after taking the tablet.

If you are in Group 2, you should take MK-2206 at about the same time each week with about 1 cup (8 ounces) of water. You must take MK-2206 at least 2 hours before or at least 2 hours after any food or a meal. You should not make up any missed doses.

If you are in Group 3, you should take MK-2206 at about the same time each week with about 1 cup (8 ounces) of water. You must take MK-2206 at least 2 hours before or at least 2 hours after eating. You should not make up any missed doses.

If you will take AZD6244 (Group 3), you should take the study drug in the morning before you eat or drink anything. You can eat breakfast 1 hour after you take the dose.

If you will take sorafenib, you must take your doses 12 hours apart. You will take 2 tablets each morning, and again each evening. Sorafenib should be taken with about 1 cup of water on an empty stomach (either 1 hour before a meal or 2 hours after a meal). If you feel nauseated before or after taking the medication, anti-nausea medications should be used. If you miss a dose, you should skip it and take the next scheduled dose at the right time.

Your medication should be stored at room temperature.

Study Visits:

The study visit schedule is described below. In certain cases, with the permission of your doctor, the study visits may occur up to 7 days earlier or later than described below.

On Day 1 of each cycle:

• You will have a complete physical exam, including measurement of your weight and vital signs.
• You will be asked about any drugs you may be taking and any side effects you may be having.
• Your performance status will be recorded.
• Blood (about 3 teaspoons) will be drawn for routine tests. If your doctor thinks it is needed, you may have to have these blood tests more often.

On Day 1 of every odd-numbered cycle (Cycles 3, 5, 7, and so on):

• You will have a CT scan and/or MRI of the chest (and abdomen if the doctor thinks it is needed) to check the status of the disease.
• You will have a chest x-ray.
• MRI of the brain (if the doctor thinks it is needed)

Additional Tests for Group 2:

• During screening, on Day 1 of Cycle 2, and at the end-of study visit, you will have an eye exam.
• On Day 1 of Cycle 1 you will have an ECG before taking your study medication and then again about 4 hours after you take your study medication.

Additional Tests for Group 3:

• During screening, on Day 1 of Cycle 2, and at the end-of study visit, you will have an eye exam.
• During Cycle 2 (Week 6 of being on study drug), on Day 1 of Cycle 4, and then every 3 months, you will have a multigated acquisition (MUGA) scan and/or echocardiogram to check your heart function. You will have these tests more often if the doctor thinks it is needed.
• On Day 1 of Cycle 1 you will have an ECG before taking your study medication and then again about 4 hours after you take your study medication.

Length of Study:

You may continue to take the study drug(s) for as long as you are benefitting. You will be taken off study if the disease gets worse or if you have intolerable side effects.

End-of-Study Visit:

When you go off study for any reason, you will have an end-of-study. This visit may occur up to 7 days earlier or later. The following tests and procedures will be performed:

• Your medical history will be recorded.
• You will have a complete physical exam, including measurement of your weight and vital signs.
• You will be asked about any drugs you may be taking and any side effects you may be having.
• Your performance status will be recorded.
• Blood (about 3 teaspoons) and urine will be collected for routine tests.
• You will have a CT scan and/or MRI of the chest (and abdomen if the doctor thinks it is needed) to check the status of the disease.
• You will have a chest x-ray.
• You will have an ECG (Group 3).

Follow-Up:

You will have a follow-up evaluation performed 4 weeks ± 7 days after therapy is discontinued. This evaluation may be a visit or contact by phone by the research personnel. If you are in Group 3, you will have a MUGA scan and/or echocardiogram to check your heart function.

You will be called every 3 months for up to 3 years and asked about any cancer treatments you may be receiving. This phone call will take about 10 minutes.

This is an investigational study. Erlotinib is FDA approved and commercially available for treatment of NSCLC that has gotten worse. Sorafenib is approved in renal cell cancer and hepatocellular carcinoma. Sorafenib has also has also been evaluated in unselected advanced patients with NSCLC both alone or with chemotherapy in the first-time treatment of patients . MK-2206, and AZD6244 are not FDA-approved or commercially available. At this time, they are only being used in research.

Up to 450 patients will take part in this multicenter study. Approximately 350 will be enrolled at MD Anderson.

Inclusion Criteria:

1. The subject has a diagnosis of pathologically confirmed NSCLC by tumor biopsy and/or fine-needle aspiration.
2. The subject has a diagnosis of either advanced, incurable stage IIIB or stage IV NSCLC, and failed at least one front-line metastatic NSCLC chemotherapy regimen, or EGFR TKI. (Subjects who have failed adjuvant or locally advanced therapy within 6 months are also eligible to participate in the study).
3. The subject has measurable NSCLC (patients with active new disease growth in previously irradiated site are eligible).
4. The subject's ECOG performance status is </= 2 at study entry.
5. The subject has biopsy accessible tumor
6. The subject has adequate hematologic function as defined by an absolute neutrophil count (ANC) >/= 1,500/mm3, platelet count >/= 100,000/mm3, WBC >/= 3,000/ mm3, and hemoglobin >/= 9 g/dL.
7. The subject has adequate hepatic function as defined by a total bilirubin level </= 1.5 x the upper limit of normal (ULN) (bilirubin >/= 1.5 x ULN with known Gilbert's disease is allowed), and alkaline phosphatase, AST and ALT </= 2.5 x the upper limit of normal or </= 5.0 x ULN if liver metastases are present.
8. Serum creatinine clearance >50ml/min, either by Cockcroft-Gault formula or 24-hour urine collection analysis
9. If subject has brain metastasis, they must have been stable (treated and/or asymptomatic) and off steroids for at least 2 weeks.
10. The subject is >/=18 years of age.
11. The subject has signed informed consent.
12. The subject is eligible if disease free from a previously treated malignancy, other than a previous NSCLC, for greater than two years. Subject with a history of prior basal cell carcinoma of the skin or pre-invasive carcinoma of the cervix are allowed.
13. Women of childbearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Childbearing potential will be defined as women who have had menses within the past 12 months, who have not had tubal ligation, hysterectomy or bilateral oophorectomy. Should a woman become pregnant or suspect that she is pregnant while participating in this study, she should inform her treating physician immediately.
14. The subject, if a man, agrees to use effective contraception or abstinence while on study and for 90 days after last dose of study drug.
15. Subject is able to swallow capsules and has no surgical or anatomical condition that will preclude the patient from swallowing and absorbing oral medications on an ongoing basis.

Exclusion Criteria:

1. The subject has received prior chemotherapy, surgery, or radiotherapy within 3 weeks of initiating study drug, or 4 weeks for bevacizumab or investigational drug or 72 hours for erlotinib or the subject has not recovered (</= Grade 1) from side effects of the prior therapy (localized palliative radiotherapy within 2 weeks is allowed).
2. The subject has undergone prior thoracic or abdominal surgery within 30 days of study entry, excluding prior diagnostic biopsy.
3. The subject has cardiac conditions as follows: uncontrolled hypertension BP > 140/90 despite optimal therapy, uncontrolled angina, ventricular arrhythmias, or congestive heart failure New York Heart Association Class II or above, baseline LVEF </= 50%, prior or current cardiomyopathy, atrial fibrillation with heart rate >100 bpm, unstable ischaemic heart disease (MI within 6 months prior to starting treatment, or angina requiring use of nitrates more than once weekly).
4. The subject has neuropathy >/= grade 2
5. The subject is pregnant (confirmed by serum b-HCG if applicable) or is breastfeeding. In the event of inconclusive pregnancy test results, the investigator will have final determination of pregnancy status.
6. Subjects will be excluded for other concurrent severe and/or uncontrolled medical disease which could compromise participation in the study (i.e., uncontrolled diabetes, severe infection requiring active treatment, severe malnutrition, chronic severe liver or renal disease).
7. Refractory nausea and vomiting, chronic gastrointestinal diseases (e.g. inflammatory bowel disease), or significant bowel resection that would preclude adequate absorption
8. Subjects with poorly controlled diabetes (HbA1c >8%) are excluded.
9. Subjects whose tumor harbors the EML4-ALK fusion gene are excluded unless the patient has failed treatment with Anaplastic Lymphoma Kinase (ALK) inhibitor.
10. Subjects are excluded if they have QTc prolongation >450 msec (Bazett's Formula) for males or >470 ms for females on screening or other factors that increase the risk of QT prolongation or arrhythmic events (e.g., heart failure, hypokalemia, family history of long QT interval syndrome) including heart failure that meets New York Heart Association (NYHA) class II or above or require use of a concomitant medication that can prolong the QT interval.
11. Subjects who have abnormal K+ or Mg++ levels will be excluded if these levels cannot be corrected to within normal range with adequate supportive treatment prior to study drug initiation.
12. Subjects whose tumor harbors an EGFR mutation are excluded unless the subject failed treatment with EGFR TKIs in which case the subject can be randomized to Arms 2, 3, and 4.
13. Drug Specific Eligibility Criteria based on Treatment Arms- Subjects are excluded from the erlotinib monotherapy arm if they have progressed on prior EGFR TKI therapy; from the AKT inhibitor arm(s) if they have received prior AKT inhibitor therapy; from the MEK inhibitor arm if they have received prior MEK inhibitor therapy; and from Sorafenib arm if they have previously received the drug or have prior history of clinically significant hemoptysis or bleeding diathesis as per principal investigator judgment.