As I see it, the main issue is sensing the hits. If it's not a MIDI drum, then your choices are going to be attaching some sort of mic to the drum shell, or if it's a kick drum, rigging up some sort of switch. The problem with the switch idea will be getting the timing right - the sound happens a few milliseconds after the switch closing.
If you want lights that are bright, it's easy enough to get LED stage lights that are controllable with DMX or some other means. Making a cylinder of light that shoots out of the drum ... mount a pin spot in front of the drum? In the drum?
You'll need smoke/fog, too, or there will be no effect.
http://www.ebay.com.au/itm/White-LED-Pin-Spot-Light-Narrow-Beam-Pinspot-DJ-Mirror-Ball-Spotlight-For-Party-/142483110496
https://www.ebay.com.au/i/380296934224?chn=ps&dispItem=1
Your best bet would be to speak to some people that actually do stage lighting. Mount something in/around the drum (if there are multiple lights, aligning them will be a nuisance, and keeping them aligned will be a challenge). Condenser mic on the shell of the drum, and a little ssoftware. All doable, but it won't be cheap.