Yes, in general electrical outlets are installed directly next to a stud.
However, apartments may have some different things going on:
- There may be metal studs. These are much harder to find by knocking.
- Outside walls especially, may be a sheet of drywall on thin strapping with concrete behind, or even the drywall right on the concrete. These walls can still have outlets (they usually install them prior to pouring), and so to hang something up, you need a hammer drill with concrete bits, and a wall plug. I'd be cautious about even using a tapcon, because you don't really know what the concrete is like underneath (poured or block - and if it's block, you may be right on a mortar joint). With a wall plug, it's mostly the drywall that will hold it up.
Do you actually need a stud? How heavy is this lamp? Certainly a stud is better, but you can always use a wall plug. Put a screw in where you suspect you have a stud and want to mount the light, and if you get it wrong, put in a plug.
If it's light enough, as you suggest, some of the adhesive-based hooks are probably good enough (assuming the light can be hung that way).