Do salt licks kill aquatic plants?

Not that I have ever experienced, but if you raise the level of salt in any body of water things that are sensitive to it will die, including fish and frogs.

I have had a lot of success with copper sulfate, but not everywhere at once, the chemical removes oxygen from the water, so applying it everywhere will leave no safe place for fish. I would treat one side of the lake with it, then in a few days the other half, that way the fish would have a safe place to go. The best ecological solution would be to buy fish that eat plants.