Lean and Six Sigma, taken together, make the toolkit available for any process improvement project much richer than either of them taken singly. Six Sigma traces its origins to the application of statistical methods in an industrial context (starting with the adoption of Statistical Quality Control at Western Electric through the pioneering efforts of Walter Shewhart) whereas Lean traces its origins to Japanese quality concepts (a lot of which came from Lean manufacturing methods used at Toyota).
Leaving apart the differences in the two methodologies, it is always a good idea to use whatever helps to improve a process- Six Sigma alone, Lean alone, Six Sigma + Lean together as well as Six Sigma + Lean + any other tool/concept. Knowing which tool/concept to use requires thoughtful consideration but once the tool/concept to use has been identified its application is perhaps relatively easier.