AZD2014 and Weekly Paclitaxel in Squamous NSCLC

Inclusion Criteria: 1. Histologically or cytologically proven squamous non-small cell lung cancer (NSCLC) where treatment with weekly paclitaxel is an appropriate treatment option. 2. Relapsed or refractory disease after at least one line of prior therapy. Subjects must have previously received appropriate line(s) of standard of care (SOC) treatment. 3. Measurable disease by RECIST v1.1 criteria 4. Life expectancy of at least 12 weeks. 5. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. Exclusion Criteria: 1. Radiotherapy (except for palliative reasons), chemotherapy, endocrine therapy, or immunotherapy during the previous 3 weeks (4 weeks for investigational medicinal products and 6 weeks for nitrosoureas and Mitomycin-C) before treatment. 2. Ongoing toxic manifestations of previous treatments. Exceptions to this are alopecia or Grade 1 toxicities which, in the opinion of the Investigator, should not exclude the patient. 3. Known leptomeningeal involvement, brain metastases or spinal cord compression. 4. History of hypersensitivity (\> Grade 2) to active or inactive excipients of AZD2014, drugs containing Cremophor, taxanes or structurally/chemically similar drugs 5. Current refractory nausea and vomiting, chronic gastrointestinal disease, inability to swallow formulated product or previous significant bowel resection that would preclude adequate absorption of AZD2014 6. Patients with Diabetes Type I or uncontrolled Type II (HbA1c \> 59 mmol/mol assessed locally) as judged by the Investigator 7. Major surgery within 4 weeks prior to entry to the study (excluding placement of vascular access), or minor surgery within 2 weeks of entry into the study and from which the patient has not yet recovered 8. Adequate hematologic function independent of transfusion and growth factor support for at least 7 days prior to screening (with the exception of pegylated G-CSF (pegfilgrastim) and darbepoetin which require at least 14 days prior to screening), defined as: * Absolute neutrophil count 1500 cells/mm3 (1.5 x 109/L) * Platelet count 100.000 cells/mm3 (100 x 109/L) * Haemoglobin 9.0 g/dL 9. Adequate hepatic and renal function defined as: * Serum aspartate transaminase (AST) or alanine transaminase (ALT) 2.5 x upper limit of normal (ULN) if no demonstrable liver metastases or 5 x ULN in the presence of liver metastases * Alkaline phosphatase (ALP) \< 5 x ULN * Serum bilirubin 1.5 x ULN (unless bilirubin rise is due to Gilbert's syndrome or of non-hepatic origin) * Estimated Creatinine Clearance 50 ml/min (Cockcroft-Gault) or serum creatinine 1.5 x ULN