Mouthguard to protect lower lip

I don't use and mouth or earguards when I am rolling, but lately I noticed than when I get put in a crank involving my jaw, a failed peruvian neck tie, 5 finger or guilotine choke, I keep on getting cuts on my lower lip due to my own lip pressing against my lower teeth. I have a shock doctor mouth guard and I started using it but it only covers my upper teeth, I guess they are the boxing style and concentrating on locking the jaw. Is there another style maybe that would cover both lines of teeth for better lip protection. Those little cuts don't heal for like 7-10 days and hurt like a bitch while training.

I know some exist
But sorry to say I dont know where to get them or how much
I thibk football mouthguards protects the bottom and top, and i know if u go to a dentistl/orthodontist u can get a custom one and they can prob make it for top and bottom

there are single mouth guards and double mouth guards, single mouth guards don't give you as much protection but you can breath and talk easier. Sounds like you need a double mouth guard you can find them at any athletic store, i picked mine up at hibbets.

close your mouth

I might not help if you're actually bitting hard down on you're lip, but just putting some lip balm on before you roll will help your lips from cracking or cutting. It's worth a try.