Locker info, per the Disney site (yes, it might not be up to date, so FWIW. I know there was no key deposit or keys when we rented lockers at MK or EP, but I could have sworn there was the option to choose small or large on the touchscreen menus)...
Lockers at Theme Parks
For your convenience, each theme park offers lockers that are available for a fee.
All-Day-Access Lockers
Rent a key-operated locker that you can access all day for a one-time fee. A $5 refundable deposit is also required for each locker key. You must return your key no later than one hour after park closing to receive your deposit.
Small lockers are available at Magic Kingdom park. Small and large lockers are available at Epcot, Disney’s Hollywood Studios and Disney’s Animal Kingdom park. Explore locker details and pricing:
Small
11" x 9" x 16"
$7/day + $5 key deposit
Large
17.5" x 12" x 16"
$9/day + $5 key deposit
Single-Use Lockers
Single-use, coin-operated lockers are located near the bus information booths at Epcot and at Disney’s Hollywood Studios. Only quarters are accepted, and payment is required for each use.
At the Epcot location, single-use lockers are 23” x 16” x 29” and the cost is $1 per use.
At the Disney’s Hollywood Studios location, single-use lockers are 4” x 5.5” x 6” and the cost is $.50 per use.
All lockers are subject to availability on a first-come, first-served basis.
Lockers at Water Parks
Each Disney water park features keyless lockers that can be used throughout the day for a one-time charge.