Stair lifts are not accepted in your local council's kerbside recycling bin, bag or box or residual bin. If it's in poor condition when dismantled it can be disposed in at your local Household Waste Recycling Centre. However if the lift is in good / fair condition these can be recycled by going back to where they were purchased from. Some NHS Trusts also accept them. You may want to consider donating it to a local charity, charity shop or community organisation.
Find out what you can recycle in your council's area or find your nearest Household Waste Recycling Centre at Recycle for Merseyside and Halton