If you need a big locker while going on a ride its a $2 charge, whereas they used to be free, so best to pack light or take a small backpack if one is needed, and hence why the new refillable mugs have a more space saving design with a screwtop lid.
I've learnt from experience that similar mugs filled up to the top will leak on their sides, but if its only 3/4 full tend to be okay, but again another good to reason to have everything in your backpack in ZipLoc bags, aside from extra protection from the weather and water rides.