It's been several years, but as I recall it was really only a minor pain in the neck:
1) As I recall, the lockers work by fingerprint. So if Dad is the one who puts the stuff in the locker, Dad has to be the one to get the stuff out of the locker. Dad can't take junior to the restroom and send Mom to retrieve the stuff from the locker.
2) Since you don't get a key, you have to remember your locker number. I take a pen and some paper so that I can write down the locker number on a small piece of paper and put it in my pocket.
There are lockers at the front of the park, where you pay and can go in and out of the locker all day. Useful if you have something heavy that you don't need to carry around (suntan lotion, poncho, spare clothes). If you are not allowed to take stuff on a ride, then there are free lockers near that ride. They might not be right next to that ride if there are several rides near each other which all require you to use a locker.