Yes. I can envisage the sort of thing you mean (I think): a metal box that you get into and it moves horizontally, a sort of travelling room basically (German has a word for lift translates literally as "rising room" though I can't remember what the word is... ). I don't think I've ever seen it though, unless you count a cable car.
Yes, I
thought the concept simple enough - the problem is finding an application where there isn't an obviously better solution. One that I think might stand up is a pedestrian level crossing between platforms on a high-intensity metro service. For example, imagine that the southern end of Thameslink was reached by turning right instead of left at Blackfriars Junction, and rebuilding the link line from Waterloo East to Waterloo rather than one above Borough Market. Ignoring any other plans for reworking Waterloo's concourse, you'd want to retain pedestrian access across your new pair of lines, and might not want to make everyone go down and up to cross.
Being at a station should remove any safety issues - it would be no more at risk of being hit by a train not stopping than another train. Assuming one of those new computer-choreogrphed
CBTC▸ metros (like Thamelink???), synchronising the "lift" with train movements shouldn't be hard either. One question I can see that would need to be confirmed is whether the limit of horizontal acceleration, so as not to have people falling over, would permit a short enough slide time.