Hello, my name is***** and I have over 20 years of experience as a veterinarian. I'm sorry to hear that your pup is suddenly licking his front paws and lips and seems lethargic.
Since this is a new behavior then dogs will often lick when they have a bad taste in their mouth but that should not last long. They can also lick when they have something caught between their teeth, an infected tooth, or something stuck on the roof of their mouth.
Have you looked at his teeth and gums and on the roof of his mouth?
Has his appetite increased or decreased recently?
Dogs will often lick when they are feeling nauseous or have gastroesophageal reflux to try and settle their stomachs. If he has had a change food or treats, ate something different or was given a lot of table scraps, or got into the garbage then he may be nauseous.
Metabolic diseases that cause stomach upset like kidney or liver disease, hyperlipidemia, or pancreatitis can cause licking. Anemia can lead to pica or eating or licking non food items.
I do recommend that he see his veterinarian for an examination and some blood tests to make sure there are no health problems behind this behavior if his licking and lethargy continue.
For now in case this is related to nausea or reflux to try and settle his stomach you can give 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 10mg tablet per 20 to 40 pounds of body weight every 24 hours.
Either of these will reduce stomach acid and should help settle his stomach. You can use these for several days if need be or even long term as they are very safe medications.
You do want to mention this behavior to his veterinarian at his next veterinary visit even if he improves with the acid reducers as they will likely want to run some blood tests to look for any possible developing problems.
It may also help to feed him a bland diet as well. A homemade bland diet consists of 1/3 boiled, lean hamburger (or boiled, white, skinless chicken) and 2/3 boiled, white rice or pasta. 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 symptoms return with a return to a regular diet then discuss using a low irritant diet like Hills i/d or Purina Veterinary Diets EN with his veterinarian.
In an older pup licking can also be a sign of pain, especially arthritis pain, and though generally they lick the sore joint not always. If he seems stiffer than usual or is limping then his veterinarian should examine his for signs of joint pain/arthritis.
Please let me know if you have any further questions.