The tire brand and model are only somewhat related to the lift, but you will need to figure out your lift height and a target tire size to accompany that, as well as how much height you can add and still fit where you park. Also take note on if there is a slope where you get into the parking structure so you can leave extra clearance and not risk your roof.
If you install a 2" lift it should be easy to run a 275/65r20 tire which is 34.1" diameter so your total height would be 2.5" taller, or you can probably do a 285/60r20 which is 33.5" diameter, maybe even 285/65r17 which is 34.6" . If your parking situation gives you room for an extra 3 inches height with room to spare you're in good shape.
But not every tire is available in every size, for example the general HTS60 is available in 275/65r20 but not 285. The Nitto tires are available in a lot of sizes. You might also find some sizes are more expensive than others if cost is a factor, like 35x12.50r20 is a pretty common size so you'll find more budget choices in that size than for example 295/60r20 even though that is a little smaller and "should" cost less just on raw materials.
Hope that helps. Kind of fun part of all this is we all have different weather and terrain and lifestyles so we have to take that into consideration when sharing experiences