When you get a locker at a WDW park, you pay a small fee and a refundable $2 deposit and get a key. The key lets you into the locker as much as you want all day; when you return it, you get the $2 deposit back.
If you hop to another park, simply return the key and hold on to your receipt. When you get to the next park, show your receipt and pay the $2 deposit again to get another locker, but you won't have to pay the whole fee again.