it’s a type of heat engine. heat engines require temperature difference to work, and the lower it becomes, the less energy is there in the first place and a very fundamental limitation, that is carnot cycle efficiency, goes down very quickly. in practice, all heat exchangers have some thermal resistance, and the lower temperature gradient you can afford to use up on this, the bigger heat exchanger becomes, making low grade heat powerplants extremely big and expensive on top of barely generating any electricity

i don’t think there’s a lot of energy to be squeezed from daily variations in air temperature vs lake temperature, you’d be better off just by using solar panels on the same area