It's called a bit key (or a barrel key if it has a hole in the end, hard to tell from the picture).
You can try to close to what you need by comparing your neighbors key to the profiles at
http://www.ilco.us/media/853776/v5/File/key-blank-directory-09-bit-barrel-sec-7.pdf. You'll see there are a number of measurements you'll need. You can get the diameter and basic shape from your neighbors key. But then you're on your own from memory when it comes to the bit shape (the part that sticks out), size, and profile.
You can buy them on line, or call around. Some locksmiths carry them, or any could order it for you. If you have a hard time locating one, you might have better luck with a locksmith in an "older" part of your city.
Or you have a locksmith come out to the shed and take a look at it.
Good luck.
