I have a stairlift in my house, for me. I don't even like it myself - they are ugly buggers! They are also very expensive, but they should not make taking things up and down stairs more difficult, except for the big furniture items like double wardrobes, beds etc. For smaller everyday items like laundry baskets, and some suitcases - depending on their size of course - you can actually carry them up and down stairs on the chair seat, or sit on the chair yourself - as long as you are mobile, a disabled person should only have themselves on the chairlift!
There is no way on Earth that I would ever ask one of my wonderful children to install one in their homes, which means that I can never visit them in their homes, but my husband and I stay at places like Travelodges, and Premier Inns when we go to visit them, as their accessible rooms and ensuites are at least always adequate. We do live several hours away from our children, so always have to stay overnight.
So there is no way that I think the OP, or anyone else, should install a stair lift for anyone not already living in their home.
However, I don't see how a downstairs toilet or a commode would be of much use to the OP's MiL, if she wanted to stay overnight, as she would also need a wetroom style shower. If she, or you if not, can afford to stay somewhere like a Premier Inn then in my mind it is a much better option. If/when things in my daughters home get too noisy or tiring (she has 3 beautiful and very cute under 5's) then I find it brilliant to be able to say how tired I feel, and then go back to the hotel, even if it is only for a little nap etc.
If necessary, I will go into residential care when/if the time comes, as I could not bear to think of how much of a burden I was being to the ones I love the most, even if it was at all pratical for me to move in with them.