There was no build for Luna available, so here's an attempt at solo mid Luna.

Luna has decent range (especially with Q) to hold mid solo while focusing on last hitting. The goal is to keep her range while farming and not taking too many hits. Obviously this requires a team that will call MIAs and allow you the free roam to farm mid. Save Q for if the enemy mid feels like pushing, while letting your minions soak up their minion damage as you last hit.