Not sure about lexan, but I think plexiglass is just a brand name of acrylic. I could be wrong though.There is a really good chance it will warp, yes.
Plexiglass is the least stable plastic sheet goods.
Acrylic is better
Lexan polycarbonite is the best. Lexan is VERY heat and humidity stable. And is not as brittle so drilling it is easy as pie.
On a side note, I shot a .22 at a scrap of Lexan from 20 yards. Blew a hole straight thru it without cracking around the hole. It won't shatter.
They are priced accordingly. Plexi being the cheapest.
A 4 x 8 sheet of Lexan runs about $150 but well worth it.
*Edit* Whoops, didn't see Lookinround's post