There's absolutely no doubt that lead dissolves in water. Water pipes used to be made of lead and people could be, and were, poisoned by their drinking water! This is worse in acid water (i.e. water with a pH lower than 6.5, commonly referred to as "soft" water).
Toxins such as lead may be absorbed by fish through the skin and mucous membranes. It is a cumulative poison that, over a period of time, may affect vital organs such as the liver. However, fish seem to have a far greater tolerance of these toxins. There are tuna swimming around in the ocean containing levels of mercury and cadmium which would kill humans!
It's all a question of scale. Given the quantity of lead weights which may be present in a lake and their extremely slow dissolution rate in a large volume of water I would imagine that it would take a very long time for fish to be affected. Certainly many times longer than their natural lifespan.
It's a good question though Tony - the sign of a thinking angler.