I'm impressed you're even riding, with all you've been through, and are still going through.
I'm not in the medical profession, so I can't say for sure, but I don't think menopause would be the cause of riding more slowly, unless the lack of estrogen has some effect on muscle fibers. There's probably so much happening in your body that is foreign to it, with the current and earlier treatments, that it could be anything. What does your blood count look like? And with a tumor in your lungs, could it be that you're not getting enough oxygen into your bloodstream? Do you have any problems with your liver, from all the medication?
I have not had your experience with cancer, just with menopause. I'm now on natural (as opposed to synthetic) hormones, which has helped me tremendously, as far as hot flashes, mood swings, appetite, and all those other symptons. It has not affected my riding speed in any way.
I imagine you've tried many things, but perhaps there's a trainer in your area that's had some clients with similar issues? Or maybe you could get some names from Lance Armstrong's website, or other cancer or sports training sites.
There must be someone out there who has faced this kind of problem. Keep searching, and let us know how you're doing.