First, I am glad to hear that his gums are pink and he doesn't appear sore when you press on his stomach since those are often associated with urgent issues. And I'd note that if he has eaten out of the cat litter box, this certainly be causing the nausea and is triggering both his lip licking and appetite loss. Though just to note we could also see this with bacterial or viral gastroenteritis, pancreatitis, parasites/protozoa infections, general dietary indiscretions, and ingestion of harmful items (ie toxins, plants, non-edible items).
With this all in mind, we can try some home supportive care to try to settle his stomach. To start, if he hasn’t just vomited (since otherwise we’d need to rest the stomach for a few hours first), you can consider treating with an OTC pet safe antacid like Pepcid (More Info/Dose @http://www.petplace.com/article/drug-library/library/over-the-counter/famotidine-pepcid), Zantac (More Info/Dose @ http://www.petplace.com/article/drug-library/library/over-the-counter/ranitidine-hcl-zantac), or Tagamet (More Info/Dose Here @ http://www.petplace.com/article/drug-library/library/over-the-counter/cimetidine-hcl-tagamet). Whichever you choose, we’d give this 20 minutes before offering food to allow absorption. Of course, do double check with your vet if he has a known health issues or is on any medications you haven't mentioned. Also if you give this and he cannot keep it down due to nausea that is usually a red flag that we need to bypass his mouth with injectable anti-vomiting medication from his vet.
Once he is more settled, you can plan to tempt with small meals of a light/easily digestible diet. Examples you can use are cooked white rice with boiled chicken, boiled white fish, or scrambled eggs, or meat baby food (garlic/onion free only) There are also OTC vet diets (ie Hill’s I/D or Royal Canin’s sensitivity) that can be used too. The aim of these diets is that they will be better tolerated/absorbed by the compromised gut. Therefore, it should get more nutrients in and result in less GI upset.
Or if he cannot be tempted but isn't vomiting, we can choose to syringe feed with a watered down calorie rich foods (ie puppy food, Hills AD, Royal Canin Recovery diet, Dogsure) to keep nutrition and fluids getting into him.
Since dehydration is a risk for Mr. Papetio (especially as those sticky gums are an early stage sign), we need to keep an eye on his hydration. To check this and make sure dehydration isn’t an issue, there are a few parameters you can test. Further to checking for gum moisture, you will want to make sure his eyes are not looking sunken and that he doesn’t have a "skin tent" when you lift the skin. To see how to check these, you can find a good video HERE (http://www.ehow.com/video_12232503_dog-dehydrated.html). If you do see any of these signs already, then that would be our cue to have him seen before this becomes an additional issue (especially since its often dehydration that makes them feel unwell).
Overall, a wide range of agents could trigger the nausea related signs we are seeing. Therefore, we’d want to start supportive care to try to settle his stomach. Though if he cannot keep that or water down at any point, appears any more dehydrated already, or doesn’t respond to the above within 12-24 hours; then we'd want to get his vet involved. They can assess his hydration, rule out fever, ensure nothing in his stomach that shouldn't be, or any sinister viruses present. Depending on their findings, his vet can treat with injectable anti-vomiting medication, fluids, +/- antibiotics to settle his stomach and get him back feeling like himself.
Please take care,
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