Only a little bit, for example Leica a bit warmer, Zeiss a bit greener. But these differences are pretty easily handled in PP. Lighting conditions, etc., will probably make more difference and need more PP effort than changing lenses will.
I once made separate profiles for a number of Leica and Zeiss M lenses and found that the differences didn't seem to have been worth the trouble of the extra profiling. It's probably sufficient to profile one most commonly used or 'average' lens, unless you have others that noticeably distort WB.
Just recently I've had a problem concerning camera profiles with Color Checker and I1: No trouble making them, but he instructions say to put them in a user library that no longer exists in latest versions of OS X. Where do you put them on a Mac? I've made several guesses, but the profiles don't appear in the drop-down list of choices in LR/ACR.
A friend has just acquired new camera profiling software (German, don't remember the software name or company) that uses 120 patches instead of the smaller number on Color Checker. We're going to re-profile soon (hoping to get regular RX1rII, A7rII and Kolari mod's WB to match). We have to figure out where to put them on Mac hard drive.
I can report back on this in a week or so.
Kirk