This doesn't provide an answer for lakes.
But I always thought the explanation was eggs randomly getting stuck to bird feet. Or maybe a bird carries a fish with eggs up there and eats it or something. Inevitably it happens though...
"Life finds a way"
- Dr. Ian Malcolm
Lakes have connected rivers and streams that provide paths for fish and eggs to move around. There are human and animal activities that affect this. Your bird example and beavers causing floods could allow movement.