When you click on links to various merchants on this site and make a purchase, this can result in this site earning a commission. Affiliate programs and affiliations include, but are not limited to, the eBay Partner Network.
Sounds like a street-only car? Get an alignment if you want even tire wear and the least amount of tramlining possible. You likely won't notice any handling difference on the street regardless.
For track, alignment is a must and rear caster is important as mentioned above.
I'd worry more about ground clearance than alignment. Without front lift it's already quite vulnerable. Adding lowered ride height you'll probably sustain lots of damage. Hope you've got good roads.
If you lower it be prepared to have the front nose repaired. I went over just a minor change in elevation leaving a parking lot entering highway and front nose scraped. Had lift on Stingray had it set for this area forgot about until it hit in Z06. Luckily not much damage I had thoughts of how much it could cost to fix if necessary. Recommend all get lift in future purchases.