I already saw your map, and I have to give you the congratulations of the well placed spots for the snipers

, but look for Brush137 (it's nothing about the lifts issue, it's just a little note), this Brush is not well built on the Grid, even if I set the Grid by 1 unit (and not the default 16 units). Try to build the brushes well built on the grid, by setting it's dimensions like 256.0000; 128.0000; 14.00000; but not like you did or scaled: 512.1452; 213.785 for example. This little note avoids many of BSP Holes problems, as HOMs too and some collision messing too.
Your map has now a lift working well and without the collision issue, and I will describe how to solve this on my tutorial about movers and stuff.
There's your map with a working lift, so you to able to make the other 2
DM-CityStreetsBlahBETA.zip
EDIT: The tutorial I promissed is already there, on Mapping category. Take a look if you want to

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