When my mom lived with me in my old house I looked into stair lifts. All the companies I tried the lifts fitted to the treads. It was a year to wait for a council fitted one. (My house was not a council one. ) The cost was very high and free servicing for a year then there was a fee after that. It would have cost over £3,000 this is 3 years ago. They said they would buy it back after we didn't need it anymore but only give me £500. Decided against it. And mom just stayed upstairs once she couldn't climb them anymore. My brother's in law's paid over £5,000. The lift broke with his mother in law on it took 2 hours for someone to come out. She couldn't walk up the stairs her husband couldn't help her due to his health.
You need to check if the person using it is stable enough to use it. An aunt of mine had rheumatoid arthritis this is going back nearly 20 years the council came out to access her and decided she needed a lift which they fitted free. It went from the living room into their bedroom. When not in use it was in the bedroom so it didn't take up room downstairs. They lived in a private house.
Does your council have a falls unit? Before my mom had to live with me they supplied her with some equipment to help with day to day living . Fitted hand rails on outside of doors and extended the hand rail outside up the steps and inside up the stairs. Supplied a frame for the toilet and side of the bed.
Community nurse was a great source she got mom a pressure cushion, 2 wheeled walkers on for downstairs and up stairs, wheelchair and commode.
When she lived with me had that equipment at my house. Also district nurse provided a pressure mattress.
Check what your council can help you with. All the things mom had done and equipment was free. She lived in a private house.
Hope this info helps.