"Lean" identifies the need for a process or activity first and if the activity adds value tries to improve on such activity through improved process flow and enhancing productivity. Six Sigma focuses specifically on eliminating process variations in output without looking into the merits of such processes in the scheme of things.
Lean, as the name suggests breaks down processes to bare bone essentials under its guiding principle that any activity or function that does not add value constitutes waste that needs elimination.
Six Sigma, on the other hand does not question whether the activity or function adds value and works under the guiding principle that any variation in existing process or output is waste.
Lean is continuous and on-going approach, under the assumption that the day-to-day changes in technology, external environment and other factors always leave room for improvement. Six Sigma, on the other hand is a project-based approach, and the Six Sigma project group disbands on achieving the set change objectives, leaving metrics or control charts to prevent roll back.