I never understood why the lifts didn't go to platform level. Why couldn't they go right to the bottom, particularly when the lifts are in and island between the platforms? What's the point of them finishing at a slightly higher level and requiring a staircase?
To expand on my previous post.
The tracks of even the deep tubes were nearly always run underneath streets, because running beneath property required paying compensation to the landowners. Bringing the lifts down between the tracks would have meant spreading them out much further and probably outside the width of the street. The lifts had entry one side and exit the other so would have had to be between two cross-passages and thus lined roughly perpendicular to the track, pushing the tracks a long way apart.
Also, as the lift shaft was vertical, it could only be underneath the station building which contained the lift motors as well as the surface level passenger facilities. This couldn't be in the middle of the street so the lifts were almost always off to the side of both tracks, with steps down from the lower landing to platform level.
As mentioned, the surface entrances to many stations having to be moved when converted to escalators. For all these reasons, even if the lift shafts and their accesses have not been blocked since a station was converted, they probably can't easily be re-purposed for step-free access. It should also be mentioned that the general expectation of universal accessibility for railway and other facilities didn't really exist until the very end of the 20th century.