Podcasts like Manager Tools/Career Tools, but for academics: Do they exist?
I spent a little while searching around various podcast directories for something like this, and came up blank. I suspect the main cause is that running a lab is really not that much different from running any other group of people, and the difference between PIs/advisors and managers really isn't that big. Because of that, anyone looking for podcasts on running a lab can look to any of a number of management podcasts and follow the advice there. If you're a bad advisor, you don't care anyways, so you're not looking for advice.

That said, I was surprised that I wasn't able to find any podcasts focusing on being an academic, rather than about the topic of academia itself. (I did find this one episode of this university-level teaching podcast, but that seems to have been a one-off episode.) Interestingly enough, someone recently posted a very similar question on reddit, with no good answers other than "Check out chronicle.com." I'm starting to suspect that the answer to your original question is "no".