There's not enough room for a lift where the current set of stairs are. It's not just the width of the doors you need to find, you need to reinforce a lift shaft and find room for the winching mechanism - and build a housing for it. Most small 'wheelchair' lifts are indoor hoists which aren't likely to be robust enough for outdoor use.
If we were sending people a mile out of their way or over dual carriage-ways, then you might be able to justify the cost of building one (which might include a compulsory purchase order to get the land required) and get public support. But, a 350m walk with no need to cross roads is no more taxing that the status quo. And given people's biggest complaints were about the lighting and cleanliness rather than the access, those are what are being resolved.