To clarify a point earlier; the original lifts installed at the Yerkes stations at the time of opening were of the 'attended' variety. They were worked by operators for the same reason that the trains were worked by drivers; there was no provision for anything else. Automatic passenger-controlled lifts were a much later concept, and cost money to install. In the case of LT, the extra cost wasn't justified until the lifts were themselves deemed 'due for replacement'.
One thing nobody has mentioned yet is that the video in question shows a time when both types of lifts were working together at Angel. Although the majority of footage focuses on the lifts installed during the late '80s (which the maintenance man attests by remarking that they have only been in place for 6 months), at 04:50 you see the older type with sliding scissor gates.
Now these 'newer lifts' are the kind that are being replaced across the network a quarter of a century later (Covent Garden, Russell Square etc.) because, as the maintenance guy says at 12:00, the lifts were originally designed for offices, not PT. So LUL thought at the time that they'd be making savings by purchasing off-the-shelf lift cars, but we're regretting it all these years later in terms of speed, reliability and size.