My dog has bad breath, licks lips, itchy mouth. Stomach or dental?

I'm sorry to hear that Monty has been having these issues. Looking at the picture, it appears that he has a very mild amounts of tartar on his fourth premolar, so I highly doubt that this is the source of his problems. Dogs often lick their lips as a result of nausea or other irritation. Rather than dental issues, I would be more concerned about stomach upset from something he ate or other internal issues, or even allergies if he also seems itchy. Kidney disease, gastrointestinal viruses, or eating something unusual can all cause nausea. Certainly try to have Monty examined by his vet as soon as you're able to, but it doesn't sound like this is an emergency situation that requires a trip to the ER. However, if he refuses to eat or drink, starts to vomit or have diarrhea, becomes lethargic, or experiences facial swelling, then these are all signs that warrant a trip to the ER. Feeding a bland diet of boiled white meat chicken and white rice until his vet visit may help to settle his stomach if he's experiencing some nausea. I hope that Monty feels better soon!