@Jim1662 Usually if there is a law suit everyone that has any connection to it is included. If they exclude the lake association, for example, the defendant could try and put the blame on association saying its their responsibility.
You said you have good insurance, but you can check with Proper Insurance that is specifically for STR, and you would specifically include the lake as a part of the policy. But that may not be good enough for your lake association.
You would need to check with a lawyer or someone qualified for advise in your area. Usually what's popular on an internet forum may not be practical or responsible in real life.