Elevators, lifts, whatever you call them be very, VERY careful. They might be dumb beasts and limited in movement but mark my words, they're powerful beasts. You go against one, you need all the cunning and firepower you can get.
Your average elevator/lift gets you in a variety of ways: traps you inside and starves you to death (they like to do that a lot in summer days when there's no one around and usually the well blocks out your phone), they crush you with their doors (those with automatics), they open when the cabin is not in position, or they crush you with the cabin or counterweight. If there are enough people in the cabin and the machine has just "woken up" (I don't like the term "gone live"), it will crush its own cabin out of sheer hatred for the fleshlings inside. Yes, I know, there are failsafe mechanism but guess what, they're still part of it so guess what happens.
Now I know what the manual says, you should go for the engine and electronics and take them out. Smart. Very smart. Usually the same place where the engine and electronics are placed will hold some other machinery and if the lift has gone live, they've done it too. Have fun facing off one or more washing machines. That's one real knife fight.
The safest way to take one out is to get two or three floors up from ground, blast the doors open and destroy the cables: you take out its ability to use the cabin and the counterweight, and you've hurt it a lot. Mind you, it can still attack you with the severed cables so watch your six. After that, fire upwards and hit its engine. Forget the controls, it can't do anything once the engine is out. You'll have to use explosive and maybe a rocket launcher or two.
Now, if it's one of those darn buildings with more than one elevator side by side, well, then it's OK to be scared.