While some British English slang uses "lift" to mean "elevator," American English uses the word elevator.
So, depending on the context, "lift" in American English can mean:
* To raise something: "I lifted the box onto the table."
* To pick someone up: "Can you lift me up from the airport?"
* To steal something: "They lifted her purse."
However, it's not used to refer to a vertical transportation device like it sometimes is in British English.