I am very sorry to hear about your pup eating grass frantically and licking his lips/swallowing.
Some dogs like the taste of grass, but also many dogs with nausea or gastroesophageal acid reflux often eat grass or foreign material to make themselves vomit. They will often swallow repeatedly and lick things trying to soothe their nausea and acid burn. If they can rid themselves of whatever is irritating their stomach that way then all is good. But when they continue to be uncomfortable then we need to stop them from eating any more grass. It becomes a vicious cycle where more grass irritates their stomach, and stomach acid refluxes and burns their esophagus, and the worse they feel, so they try to eat more grass.
Possible causes of nausea and abdominal pain include a sudden change in diet, dietary sensitivities or allergies, or eating things that they should not like too many fatty table scraps or garbage, bones etc. Addison's which is a poorly functioning adrenal gland is another possibility for waxing and waning vomiting and nausea. Metabolic organ failures (kidney or liver disease), pancreatitis, inflammatory bowel disease or even infiltrative cancers are possible causes as well.
Has he eaten anything he should not have recently (toy pieces, bones, garbage)?
Any changes in food or treats?
You can give him an acid reducers to try and settle his stomach. Either:
1) Pepcid-ac (famotidine) at a dose of one 10mg tablet per 20 to 40 pounds of body weight every 12 hours.
2) Prilosec (omeprazole) at a dose of one 20mg tablet per 40 to 80 pounds of body weight every 24 hours.
These will reduce stomach acid and could help settle his stomach. These can be used for several days if necessary as they are very safe.
I'd also pick up his food and water for now. A couple hours after one of the acid reducers you can offer small amounts of water or ice cubes to lick.
No food for 12 hours. Small amounts of water only.
After his food fast then start a bland diet of 1/3 boiled, lean hamburger (or boiled, white, skinless chicken) and 2/3 boiled white rice. Give small meals several times a day. Feed the bland diet for several days, then start mixing in his regular diet and slowly convert him back.
If his nausea and abdominal pain continues then he may need injectable medication from his veterinarian to get his stomach upset under control.
So watch him for continued symptoms even with the acid reducers, blood in his stool or vomit or a fever (more than 103.5F rectally), a tense painful belly or lack of appetite after his food fast. If any of those occur it is time to seek hands on veterinary care.
If this has been a repeated problem for him consider whether he has been getting different treats or lots of table food, or have you been feeding a different diet?
He may have a dietary allergy or a sensitive stomach.
If he has this problem continually it would also be a good idea to have blood tests done as well to make sure there isn't an underlying metabolic problem like early organ failure, pancreatitis or Addison's disease present.
Please let me know if you have any further questions.