There are a number of factors that lead to the development and intensity of lake effect snow.
Below I have listed (in order of importance) the factors needed for LES and then most of the factors that determine intensity.
Factors needed to make LES:
1) An open body of water that cold air can travel over to pick up heat and moisture from. In most cases, the air needs to travel over at least 35-40 miles of water to produce LES of significance.
2) A large enough temperature difference (delta T) between the waters surface and the air at around 5000 feet. This delta T needs to be at least 13 degrees Celsius.
Some factors the determine the intensity of the snow:
1) The stability of the atmosphere from the surface to 15,000 feet. The more unstable, the heavier the snow. Also the more moisture that is already in the air before it travels over the lake, the heavier the LES.
2) The fetch or distance the air travels over the water. The greater the fetch, the heavier the snow,
3) Changes in elevation once the LES clouds hit land. A larger increase in elevation leads to heavier snow than a more subtle increase in elevation.
4) Temperature. Contrary to belief, the colder the air is, does not necessarily produce heavier LES. As the air temp starts to drop below around 10 degrees, it becomes less favorable to producing heavy LES. Flake size is typically smaller when the air is very cold and leads to lower LES amounts.
5) Convergence of winds near the surface. Wind that converge near the surface will enhance the lifting of the air. That lifting of the air then can increase the intensity of the LES. These areas of heavier snow within a broader area of LES are called "convergence bands". Snowfall rates of 3-6" per hour are not unheard of in convergence bands.
Hope this helps!
-John