"In the lake"- inside the lake, below the surface.
The food of twenty-six species of non-cichlid fishes in the Lake
Victoria basin is described.
"On the lake"- on the surface of the lake.
Before you go boating on Lake George, please read the regulations and
rules - they are slightly different than other lakes in New York
Find all the resources you need to enjoy boating on the lake.
As for your last question:
could "on the lake" mean something is there around the perimeter of a
the usage of "on" would fit in certain contexts. As Jim suggests in the comments below, you can have a cottage on the lake where the cottage is not a house boat. But in my opinion, this is fairly debatable. I would rather use "cottage by the lake".
CORBET, P. S. (1961), THE FOOD OF NON-CICHLID FISHES IN THE LAKE VICTORIA BASIN, WITH REMARKS ON THEIR EVOLUTION AND ADAPTATION TO LACUSTRINE CONDITIONS. Proceedings of the Zoological Society of London, 136: 1–101. doi: 10.1111/j.1469-7998.1961.tb06080.x