Mom is 94 1/2. She can't do sit-ups, won't walk outside esp. during this past brutal winter. We could get her a lift chair but I feel that will not help improve muscle strength. I feel she needs to have to try to get up on her own. Today she could not get up off couch, even with my brother's help. So....get her a lift chair or not?
All kidding aside, see to your mom's happiness and comfort. Be prepared for things to change and for her to need more assistance with ADLs. (Activities of daily living). Expect some reduced mobility and ability to transfer unassisted and plan ahead.
See if you can rent a lift-chair. Depending on how fast or slow her dementia progresses, it may not be worth buying outright. My mother went from unwilling to get up to unable to get up in a few short months. She is now a two-person assist to get up, out of bed, into a wheelchair, and onto the toilet. That is, a two-person assist when she will allow anyone to touch her.
The next thing to plan ahead for is refusal to bathe or change clothes. General refusal to cooperate. It is not a mean streak. It's brain changes. There are a lot of ideas about bathing on this site and from Teepa Snow on Youtube.
You might get her to be more active with a visiting physical/occupational therapist that her doctor can prescribe.
Our doctors have always said to avoid the lift chairs for as long as possible, because that only is a bandaid for that activity, sitting in that chair. They will completely lose the ability to use their knees and muscles and not be able to rise from any chair or toilet, for example. Better that you research the methods to assist her in using her own leverage to stand. You will have to remind her each time probably, depending on her level of dementia. She needs a proper chair height, with arms that extend to the front of the seat. She will skootch (a technical term, ha ha) out to the edge of the seat, placing her feet beneath her knees and using the arm rests, push up. There are videos demonstrating this on you tube. Be sure she has arms for the toilet, there are many varieties available or rails on the wall.
A physical or occupational therapist would be a very good idea, too.
Some hospitals have gyms in them that are less scary than a public gym and she might be able to go and ride the bicycles or walk on the treadmill at a slow pace. They have people who work there who could help her. Check into that.