I'm in my early 40's so I guess I qualify
My training isn't all the different per se than what I did in my earlier years - I mean the approach is different but I'm not doing less reps, resting more, lighter weight or anything of that nature just because I'm older. If anything I train harder now than I ever have and in a week or so about to embark on one of the more difficult programs that I've read about.
I'm a lot smarter than I was before - but I could've acquired that knowledge in my teens if only the internet was invented back then
I do get an occasional ache and pain that takes longer to go away and to be honest I need to learn to listen to my body and back off when necessary. I also stretch a lot more than I used to prior to my workout and want to be more diligent about stretching afterwards.
Anyway, I'm not sure what your training's been like since you've started lifting, but I guess my point is there's no reason you can't train like anybody else - learning the big lifts and trying to get better and better at them.