This is an open-label, phase 2a, multi-centre, single-arm study to assess the efficacy and safety of the combination of AZD2014 and weekly paclitaxel in patients with squamous non-small cell lung cancer (NSCLC) that is relapsed or refractory to conventional treatment after at least 1 prior treatment with standard of care (SOC) and for whom weekly paclitaxel treatment is an appropriate treatment choice.