I personally would not introduce anything from one of the Great Lakes into my compost or anywhere else in my yard.

I would suspect there's a good chance there could be toxic chemicals and other sources of pollution in it.

At the very least, you could contact the government agency responsible for the lake to see if you could get information on the pollution levels. Then you could make an informed choice.

Alternatively, if you need more material for your compost pile, you possibly have neighbours that throw good compost material away, and they may be glad to give it to you instead.

Some people that have not been paying attention to recent information about the great lakes waters may not be aware that what we were seeing, pollutants, in the 1960
s and 1970's have been pretty much cleared out and the water is not only okay to swim in but t drink once again, so yes you can use those "weeds" that get washed up on shore in your garden depending on what they are. More than likely, if these are long and stringy they grow on the bottom and are not the toxic algae blooms that have been appearing of late.
For a large number of reason people are warned not to eat some of the fish, from the great lakes and all of the oceans of the world as well, more than a certain number of times per week.