Is it legal to smoke weed on lake Michigan?

Nope. All of Lake Michigan is within US legal jurisdiction.

Lake Michigan is the only one of the Great Lakes that is entirely within the United States, so Canada's laws don't apply to any part of it. However, all the US states that touch it allow medical use. So if it's for your glaucoma you're good to go.

No. Lake Michigan is one of the five Great Lakes of North America and the only one located entirely within the United States. The others you can on the Canadian parts.

Lake Michigan is shared, from west to east, by the U.S. states of Wisconsin, Illinois, Indiana, and Michigan. Michigan you can legally possess cannabis however it is still against federal law.

Yes. Maybe. Depends on which police department catches you. If it's the michigan police, then it's legal in michigan. I don't recall Chicago or wiscon, but whatever laws they have.

Most likely it's the cost guard. So it's federal, and weed is still illegal for the federal government.

Nowhere in the United States is the possession of marijuana legal. Some states might have removed it from their penal codes, but the federal government still prohibits its possession, and their laws extend everywhere they have jurisdiction, which includes Lake Michigan. This will be particularly true if the area of Lake Michigan where you are is a national park or preserve.