Industrial Engineering is not that hard for an ME. Just as welding is easy; ask any chipper.
Okay, you have little specialized training, but there's no reason you can'd do something useful.
In the context of a manufacturing floor, 'lean' means few people present. Doing that effectively means that every job is covered, somehow, all the time, often with 'teams', in which people are cross- trained. Nobody has to know everything, but everyone needs to be able to do at least two jobs well.
I suspect that your company's design process is 'taking too long', in someone's opinion, because it's too lean already, somewhere, and the heavy hitter with the opinion doesn't know where.
You might be able to help out by identifying the bottleneck. If you can find a high- resolution, e.g., daily, measure of the design operation's output, you may be able to correlate it with the presence or absence of particular people. If the whole shop comes to a halt when Jim is out, you'd better get a second Jim.
Maybe you can work back in time by correlating retained records of your output measure with attendance records.
Better gig: Work forward in time, by establishing a measure, then go around the department a person at a time and give each one a paid day off "starting now, and here are tickets to today's ball game".
Seize the day, and have fun with it.
-Mike-