The best time to lime the lawn is before planting seeds on prepared soil. Lime can be applied any time to a lawn that is already growing.
For a lawn that is already growing, fall is the best time to spread lime, unless it is a very wet, rainy fall season. Then, winter or spring is better, so the lime can be spread evenly on the frozen ground and can seep into the soil with the melted ice and snow or the early spring rains, as the dirt thaws. Summer is the least desirable time to apply lime to the lawn, but even then, it won't hurt anything.