The larger rentable lockers MIGHT hold a carry-on sized bag, but that's it. If you're staying at a hotel - Disney or not - most have concierge desks that will check luggage for guests before they check-in and after they check-out.
I saw some Japanese tourist roll their luggage, maybe there is a place. Call customer service at Disney.
There is stroller parking but thats all I know
They have lockers for rent, but im not sure if theyd be big enough to hold luggage.
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