Lift, being one of those verbs like "run," has quite a few definitions. The most common (as webster 1913 points out) is the actual process of lifting something up. There are more interesting definitions, however.

In aviation terms, lift is the primary force that results in flight. It is generated by the wings of the aircraft, which is in turn caused by Bernoulli's principle (which dictates the theory of flight). Lift's arch-nemesis and opposite is known as weight. If the lift of the aircraft is greater than the weight, the aircraft flies (generally speaking).

The Urban Dictionary (urbandictionary.com) states:
To steal; see also: Gank.

Example of usage:
P1: Man, I want this but I only have a buck.
P2: Lift it!
To agree with them, the American Underworld Dictionary (1950) also states:
1. Pocket picking. 2. Truck robbery, usually of petty consumers' goods; hijacking. 3. Shoplifting. 4. Armed robbery. 5. A pickpocket. 6. A truck robber or hijacker. 7. A shoplifter.
"Lift" is also the name of a song by Radiohead, a song that was not released on any of their albums but can be found online (they occasionally perform it at concerts). I will quote a brief excerpt:
This is the place
Sit down, you're safe now
You've been stuck in a lift
We've been trying to reach you, Thom

This is the place
It won't hurt, it will not hurt

A smell of recognition
A face you barely loved
Empty all your pockets
Cos it's time to go home


Sources: Thanks to pukesick for the American Underworld Dictionary reference.