I didn't find dimensions...but found this at the affordabledisney site:
... what size are the lockers and the price for rental?
Each theme park and the Transportation and Ticket Center have lockers that rent for $5 (includes a $2 refundable deposit). If you have some items that won't fit in the locker, give them to the locker attendant at Guest Relations at MGM.
If you plan to park hop, you don't have to pay another locker deposit. See the locker attendant for particulars.
I also found this on someone's trip report:
I got to the Magic Kingdom and went to the bus station to check on the size of the lockers as I planned to bring my bag the last day and leave from the Contemporary. They didn't seem big enough. I checked at the desk, and they had storage for larger items for $3.00. No problem, my plan would work.