Lean has its roots in the Just in Time and Continuous Flow days of the 1970s. Supporting the implementations and solving problems back then was the job of the TQM folks using one of many multi-step problem solving processes. We had the TQ people and the JIT people, who generally talked, but walked down different paths.
The programs were considered to be separate, but complimetary. So when the Six Sigma bandwagon started up in the 1980s and Lean started its rebirth in the 1990s we once again had two separate initiatives. This generally put a strain on resources. There was also a misconception that Lean was easier than Six Sigma and we better start with Lean first. Once we clean up our act maybe we will be ready for Six Sigma.
Once again, organizations were missing the point. Six Sigma is only two things (the zealots may disagree, but hear me out)
The tools to support the problem solving process come from many other disciplines and previous improvement programs and initiatives.
Six Sigma did not invent Statistics, SPC, DOE, Process Mapping, Brainstorming, Kano Modeling, Voice of the Customer Analysis, Benchmarking, and so on.
Lean has a toolkit that comes from the Toyota Production System, JIT, Continuous Flow, SMED, 5s, Value Stream Mapping, Kanban inventory management, and so on.
It gets back to my earlier premis that Six Sigma has a structured improvement process and a universal performance measure and uses tools to tackle issues from many resources. So, add the Lean Toolkit as well.
We should always utilize the "Best Practice Tools" that are required to tackle the issues we are facing! Who cares what discipline they came from. Integration is the key to success and Lean Six Sigma is the new buzzword.