If your screen broke on your LG enV2 can you get a new one for free?

No you cannot, as it falls under Physical Damage, which isn't covered under warranty. If you have insurance on the phone, you can pay the $50 deductible for a new one, which they will overnight to you Priority Mail.

I'm having to go through this right now. I recommend getting a belt holder style case for your new phone, I know I'll be wearing one.