Welcome to the forum. Like your cousin, I also have stage IV prostate cancer, with skeletal and soft tissue metastases. The triptorelin is very important and your cousin should keep taking it on schedule. This drug stops production of testosterone which the cancer uses as food, and thereby prevents the tumors from growing. It is possible to shrink the tumors and bone mets and relieve pain, with continued use of triptorelin.
Here in the U.S.A. doctors often add two more drugs to triptorelin: an AR5 inhibitor like Bicalutamide or Flutamide (this molecule prevents the adrenal glands from producing testosterone and also prevents tumors from uptaking any free testosterone in the system) and Dutasteride, which prevents conversion of testosterone to the more potent cancer fuel, di-hydro testosterone. Using these three drugs in combination is referred to as triple androgen blockade and many oncologists believe the combination is more effective than triptorelin alone. Bicalutamide is easier on the digestion than Flutamide.
Your cousin will probably respond well to triptorelin, with or without the other two drugs. After two years on triptorelin he will probably be able to take time off the drugs, until his PSA score rises to 8 or so, and then it will be time to resume treatment. (What was his PSA score in January when he was diagnosed? What is his PSA score now?)
I have an aggressive cancer which bounced right back after radiation treatment and two and a half years of triple androgen blockade. The disease began doubling every 24 days and it was too early to resume anti-androgens. I was able to halt the disease for a time with DCA, my notes are here:
So to answer your question, I am not aware of any reason not to take DCA while on anti-androgen therapy (triptorelin). However, triptorelin is so effective that I see no need to combine the two. He might reserve DCA for his time off the androgen blockade. It is important to remember that triptorelin is the most powerful available treatment and he should continue taking this on schedule. Also, he might ask his oncologist about adding Bicalutamide and Dutasteride. (Before beginning Bicalutamide he will want to have his breast buds irradiated to prevent gynecomastia.)
Best wishes to you both,