Thompson Lake on Bois Blanc Island in Lake Michigan has a small lake.  (Michigan, USA)

Drummond Island in Lake Huron has a couple of lakes with unnamed islands.  Fourth Lake appears to have an island with a small pond inside. (Michigan, USA)

https://www.google.com/maps/search/%5C/@46.0060905,-83.5588442,15.38z

Bog Lake on Madeline Island in Lake Superior has a couple of small islands.  (Wisconsin, USA)

https://www.google.com/maps/search/%5C/@46.8507052,-90.5886229,15.48z

A classic example is Ryan Island (also tiny Teakettle island and others) in Siskiwit Lake on Isle Royale in Lake Superior.  (Michigan, USA)  There are other Lakes on this island with islands on them.

https://www.google.com/maps/search/%5C/@48.0073129,-88.7746929,15.44z

On to Canada:

A couple of lakes on St. Ignace Island in Lake Superior have islands.

https://www.google.com/maps/search/%5C/@48.7958941,-88.0046016,13.44z

The one you maybe were thinking of is Treasure Island on Lake Mindemoya on Manitoulin Island in Lake Huron.

https://www.google.com/maps/search/%5C/@45.7071957,-82.2204366,11.07z

If you really want to go down the rabbit hole here:

http://www.elbruz.org/special-projects/islands-and-lakes/

https://www.worldatlas.com/articles/the-largest-lake-islands-in-the-world.html

https://twentytwowords.com/vulcan-point-is-an-island-in-a-lake-on-an-island-in-a-lake-on-an-island-if-you-didnt-follow-that-check-this-out/