Mr 229 -
You really only want to set your dies
once. The wisdom of that statement will become obvious the more you work with them. True, you may have to go back and tweak from time to time, but you want to avoid gross adjustments every time you go to reload. If you can't, you'll soon tire of reloading and say THWI.
We certainly don't want that outcome.
You only said "Lee Turret", but not which one. If your machine has the removable die holders like one of these things...
....then buy some of those
and then leave each set of dies set-up in that holder permanently. In that way you are simply swapping die holders to swap calibers. Follow ?
If you have to remove individual dies to change calibers, then you're going to need to swap out your lock rings for some different types that stay put when the die is withdrawn from the press. I would suggest Hornady, which come in a handy multi-pack.
HERE Using these, you can remove the die if you need. Then on re-install simply run them down until they bottom out on the lock ring and you'll be set to go again. No readjustment necessary.
All the above would seem to me to be prudent FIRST steps (ie the place to start), especially if die set-up is a quandary and not especially something that you're able to do fast. I say that because we generally refer to this hobby as "reloading" and not "die setup".
The first one is fun; the second can become a headache.
So if you can do something along these lines FIRST, then you'll never have to re-visit this again.