In Chicago I’ve observed and measured a consistent 0.8kn (1.48 km/hr) current set flowing north after a long week of consistent breezes out of the north. The water just piles up in the shallow end of the lake and when the breeze dies that water needs to go somewhere.
Lake Michigan has the least turnover of all the lakes and when thinking about predicting current on it it’s good to imagine a 300 mile long bathtub.