You can replace "lifting weights" by many different type of exercises that suits you (walk, run, bike, ...). What matters is movement, that's why it's harder to stand still than to walk, the body use the contraction of muscle to do a lot of things
If you have weak back muscles, for example, walking is not going to do that much for them - but weight lifting will.
If your quads have atrophied because of a past knee injury, just walking - even very actively - will not fix them (bitter experience here) and the injury may well recur. But gentle goblet squats and light leg presses combined with balance exercises for proprioception will sort that out.
You lose a lot of muscle when you get older, and if you have any injuries you will naturally tend to avoid specific movements in your daily life. This _is_ better addressed by weight training (ideally with physio guidence) rather than just aiming for a goal of "being active".
Either way, exercise is better than not, but lifting weights is also better than running in many regards. Been a while since I read about this so I'm struggling to remember specifics - hopefully somebody will come along and expand upon this.
I've been relatively active my whole life, and it wasn't until I started lifting weights (mostly pull ups and chin ups) where I actually started to see a difference.
A lot of people in wealthier countries work until retirement age and then park their asses on the sofa to spend the remaining years watching (awful) TV and getting fat and unhealthy. That's not living, and it's a guaranteed path to sadness (and frustration for the children who have to help the parent). Not to say that children shouldn't give back and help the parents, but it's still super important for all parties involved to be making effort.