Lake-effect snow is formed by cold air flowing over warm lake water.
The warm lake water transfers its heat into the air's bottom layer. This is done by evaporating lake moisture into the cold air right above the surface of the lake.
Warm air is lighter and less dense than cold air -- therefore the heated air then rises and begins to cool off in the colder air above.
As the air cools, the moisture from the lake that was evaporated into the air condenses and forms clouds.
If the air is humid enough where the clouds are forming then snow can be created and will begin to fall from the cloud.