I am sorry to hear that Loki is eating poorly, and is lethargic.
I understand that he has a history of arthritis and is taking Meloxicam.
Meloxicam is a nonsteroidal anti-inflammatory that is often very effective at reducing pain and inflammation from arthritic joints. Long term use however it can be hard on his gastrointestinal tract (causing irritation and ulcers) and his kidneys and liver (possibly causing organ failure).
His poor appetite and lethargy, but still drinking, concern me and I would recommend he see his veterinarian to check some blood tests to evaluate kidney and liver function. Dogs with organ damage often have a poor appetite, yet the drive to drink more.
Have his stools looked dark in color and/or runny/tarry? If so that can be indicative of gastrointestinal irritation and bleeding.
It would be reasonable to try an acid reducer to settle his stomach, you can give either:
1) Pepcid ac (famotidine) at a dose of one 10mg tablet per 20-40 pounds of body weight every 12 hours
2) Prilosec (omeprazole) at a dose of one 20mg tablet per 40-80 pounds of body weight every 24 hours
These are acid reducers and should help him feel less nauseous. Both are quite safe and either one can be used for several days if needed.
To stimulate his appetite you can feed a bland diet for the next few days. A homemade bland diet is a mix of 1/3 boiled, minced, white skinless chicken or lean, boiled hamburger and 2/3 boiled, white rice or well cooked pasta, mixed with some low salt chicken or beef broth to make it easy to lap up and swallow. Feed small meals frequently.
Then I recommend that he be examined as soon as possible.