Six Sigma is data driven problem solving. Six Sigma's DMAIC problem solving approach is simple and logical. Through understanding and adhering to its simplistic nature one can successfully solve manufacturing and service problems.
A process that is Lean is one that delivers products or services that the customer wants, at a price that reflects only the value that the customer is willing to pay for.
The combination of Six Sigma and Lean produces a system called Lean Six Sigma (LSS). LSS as defined by Michael L George in his book, Lean Six Sigma for Service, is a "business improvement methodology that maximizes shareholder value by achieving the fastest rate of improvement in customer satisfaction, cost, quality, process speed, and invested capital."
Lean Six Sigma use the DMAIC structure.
The above material is from a resource written by Quentin Brook, "Lean Six Sigma & Minitab: The Complete Toolbox Guide for all Lean Six Sigma Practitioners."