Scott, you sound exactly like me when I first started Lupron. I am an Internist and understand these things a bit more than most.
Please ask your Oncologist to drastically decrease your dose of Lupron. Try the 3monthly dose which is less than half of what you seem to be getting now. Decreasing the dose helped me tremendously without affecting the efficacy of the drug. I remained hormone sensitive for about three years and was able to continue to work 12 hours a week to date doing consults in my practice.
By all means see the Psychiatrist and the mental health team for all else they bring to the table.
Stop the starvation diet and find a way to accept the fact that your sex life will most likely never be the same. The brain is your most important sex organ and the diagnosis and treatment of prostate cancer primarily robs you of libido. In my case, a naked woman or even erotica might as well be covered furniture.
I would quit the gym. Do as much walking as you can but don’t exhaust yourself.
Remember, we are very lucky to be living in this Universe at this time, the probability is in the trillions of trillions, so ride it out. You can still find some joy once your maintenance treatment is adjusted to manageable doses.