Sherral, as long as you are working with a PC and not a MacIntosh this should work.
Right mouse click on the really cute avatar that Lizza made you and a menu will appear. Click on the "Save Image As" (it may say "Save Picture As" depending on what version of Windows you are running) and then save it like you would any other file somewhere you can find it again. Once it's saved, come into your User CP, Edit Options and Browse to where you saved the avatar and open it like you did for your current avatar. The trick is the right clicking on the picture you want to save.
Hope this helps!