The subjects who take part in this clinical research study have advanced non-small cell lung cancer (NSCLC) that has been previously treated with other drugs. If they join this study, they would receive ramucirumab (Cyramza ®) in combination with nab-paclitaxel (Abraxane®). Ramucirumab given with nab-paclitaxel is considered an investigational drug combination to use in this type of cancer because giving these two drugs together has not been approved by any regulatory authority like the US Food and Drug Administration (FDA) for NSCLC cancer. Ramucirumab works by slowing or stopping the growth of cancer cells. Nab-Paclitaxel works by blocking the ability of cancer cells to break down the internal 'skeleton' that allows them to divide and multiply. With the skeleton still in place, the cells cannot divide and they eventually die.