The result is lake effect snow. Lake effect snow tends to be confined to a small geographic known as the snowbelt. Lake effect snow can fall even when the barometer is high. Non-lake effect snow is sometimes called synoptic snow because it results from a larger scale low pressure system or from warmer air riding up and over a dome of cold air. Lightning is common with lake effect snow.
Lightning can strike whenever liquid water droplets and frozen water crystals are present.
In thunderstorms, ice crystals are in the top of the cloud with water droplets in the lower half. One charge tends to accumulate near the top of the thunder cloud. The opposite charge accumulates near the bottom. Lightning is just a spark between opposite charges. Lake effect snow often contains water droplets as well as ice crystals, especially when the lake is very warm.