We had a similar case that responded well to Xiao Chai Hu Tang (Minor Bupleurum). If you can get something on board that can control the calcium levels, XCHT can significantly help out with the symptoms you describe and potentially also the lymphoma.
That's the first thing I would try. It'll maybe take a week or two to see substantial change. If you do acupuncture, needling GB points like GB 25 and 34 (or even acupressure here) might settle his stomach more quickly.
Good luck, Angie.
Steve