Although you can have intense lightning storms on an exomoon, you would have problems maintaining this structure over a long period of time.
Setup For Exomoon With Intense Lightning Storms
Let us build our exomoon on the model of the planet in our solar system which has the most violent electric storms: Saturn. This planet is basically a lightning and storms factory with wind speeds approaching 1600 km/h (470 km/h being the fastest recorded on Earth).
Saturn is cold, very cold on one side (the night side) and somewhat lesser cold on the other side (the day side). And it is made entirely of gas. So let us give your exomoon these two characteristics: temperature difference between two hemispheres and a thick atmosphere. It would help if the atmosphere is made up mostly of hydrogen with traces of gases which get ionized easily: water vapor, ammonia, sulfur dioxide, carbon dioxide, hydrogen chloride.
In order to get extensive lightning storms, we would want to get massive tornadoes and hurricanes in the atmosphere, which can be accomplished by having a temperature difference between the hemispheres. How you get to give it this temperature difference is up to you.
Once we have massive eddies and tornadoes (thick atmosphere + temperature difference), the water vapor, sulfur dioxide, hydrogen chloride would get ionized and you would begin to see massive electric storms rolling all over the planet.
However, I'm afraid to say that things cannot go on this way for too long, unless the moon's solid surface is massive enough to hold on tightly to the atmosphere. Otherwise, it is more than likely that the atmosphere of the exomoon will gradually blow away and probably be captured by the parent planet.