You have a wonderful goal! It is good that you understand it can take time to work up to this trip. I recommend that you think in terms of several years, not decades, because (a) after 50, most people don't get better physically, they just manage not to get worse and (b) unexpected things happen.
As for what kind of physical and spiritual training you require: You don't say if you have any high altitude experience. In his good answer, Charlie Brumbaugh says that the trail starts at 15,000 feet and includes an 18,000 foot pass. Experience hiking and sleeping at altitudes of 10,000 to 13,000 feet is essential (and higher, if you can). You can easily find long hikes in this range in Colorado and California.
Why do I think this is essential? Some people, even if they are very fit, are miserable at altitude and if you are one of them, you don't want to find it out in Tibet. This is of those low probablility//unacceptable consequences cases.
As for spiritual: this isn't exactly spiritual, but you should find out how much more you can do -- and how to do it -- when you yearn to just stop. You'll figure this out for yourself by carrying a modest pack at altitude.
If you are going with a group, you need to understand what you can do. Can you keep up with the group schedule? Will you have fun? If all your experience is at sea-level, you won't know.
I envy you having this in your future.
Afterthought: You don't mention your tolerance for hard beds or no beds, being dirty, peeing and pooping behind a rock, less than gourmet cuisine....you can figure this out at sea level, but you need to know. And of course, you need to be aerobically fit at sea level.