The Lake Michigan "equivalent" of Buffalo, so to speak, would be roughly between Gary-Michigan City (or maybe into the extreme sw corner of MI) where you can just firehose it in there in a single band with rates of several inches per hour when LES parameters are very good. The problem is that the duration is more limited, so it doesn't rack up the insane totals that the Buffalo area can get. It can pile up quickly while it lasts though --- recall Michigan City receiving about 30" on 12/19/04.
I've been in 4-5" per hour on a couple of occasions with LES off of southern Lake Michigan. Didn't have thunder then, but I really didn't care lol