Such a thermal will be a cooler thermal than those not downwind of a lake. That is, it wouldn't have formed except for the localized area of cool air. Thermals form as the surface air is cooled due to a sea breeze, forcing the warm air aloft. As the sea breeze moves inland, so does the line of lift. As the line of cool air moves inland, the pockets of warm air release into the cool air that had just passed above.
Thermals form due to a convergence of cool air and warm air.
Don't be intimidated by the adiabat chart. If you can learn to fly a glider, it won't take you more than a few minutes to learn how to use this effectively. It does take a bit of practice, because the slightest change will produce vastly different results. So use it on a regular basis, and you will be able to confidently predict thermals. Thermals are parcels of air, which are forced to rise to higher altitudes because they are warmer than the air surrounding them.