Lean is a collection of techniques gathered over time that are based on observation and common sense used to do things in the most efficient way.
Six Sigma is not necessarily common sense like Lean but is a rigorous methodology of team brainstorming combined with statistical analysis assisted with Minitab or other software. Some of the tools overlap with Lean tools.
Use purely Lean if you do not know how to reduce the waste, time and bottlenecks in a process.
Use Six Sigma if you do not know the root causes of defects, process variations, and quality issues.
Use Lean Six Sigma if your project is a combination of the above two issues.