It really depends on the year. For not being in a lake belt, our weather still is greatly affected by the lakes. We always get mood flakes anytime there's a cold frontal passage while it's often clear by you. But whether or not it's a bunch of traces or something more depends on flow, fetch, etc. Rarely can we say a significant percentage of our seasonal snowfall came from LES, but the two most generous lake seasons for DTW off the top of my head are 2006-07 & 2016-17. I would say the most difficult aspect of trying to decipher synoptic from LES is so many times cold fronts or clippers, which would have a certain amount of synoptic with them to begin with, get "lake enhanced", boosting totals in MI.
In analyzing this year's totals, since everything is fresh enough in memory, of the 37" I estimate around 4-5" has been LES and maybe another few inches lake enhanced. Most of our snow has been synoptic, most of it wet.
It's probably very realistic to assume the difference in snowfall average between DTW (45") and ORD (38") is LES