Thanks for your questions! Yes you are right. Mostly for Experienced Hires in the field of management consulting, it refers to attracting candidates with solid and extensive experience in the particular field, but not necessarily management consulting experience. If you are with such experience and are a strong problem-solver, plus better if you take an MBA from a prestigious business school, you may find it smoother to get into management consulting than when you are a fresh graduate.

For "Lean Six Sigma", it is a tool for someone to identify and solve problems. If you are somehow exposed to "Design Thinking" during your university times, you can consider both as tools for one to identify and solve problems with steps and structure. It is quite a transferrable certification that you may want to explore more on free channels eg YouTube / other MOOCs even if you are not getting into the management consulting industry.

Oh btw, if you later prepare for your interviews for the management consulting positions, you may find this course helpful: https://www.onmygrad.com/course/81