Unless you're driving to LP, it's easiest to just pack your skates in your luggage and put them in the locker once you pay for it and get the combo. That's why I mentioned the cheap cloth grocery bag. It doesn't take much space in your suitcase.
I don't think I've seen anyone bring a skate bag unless they're a local. When there was a large kid's camp at the same time, you'd see Zuca's , but kids don't use the dressing room. Or at least they didn't.
The skate camp for kids last year was much,much smaller. I was told it's because the school year now starts earlier, so kids can't come in the end of August. I also haven't seen kids hockey camps or synchro camps for the last couple of years. That means more ice time for adults! Maybe in the future they'll fill the time up with adult hockey camps.