How can I stop things from falling off lazy Susan cabinets?

Here's one with raised sides:

https://www.pinterest.com/pin/191262315408120735/

if I understand your question correctly, your lazy Susan’s are not turning correctly any more? If this is correct, answering your question could vary some depending on the brand of Lazy Susan kit you have? Let’s start with the one I know of that is hopefully what you have? Your pole in the middle of your shelves is or should be two poles one inside the other so they can slip and be raised or lowered to different heights. There should be a set screw close to where both pipes come together.. lessen the screw just enough that the pole will slide up and down. Now look up underneath in the cabinet with a flashlight and you should see a mount with a pin sticking down maybe a inch or so. You need to slide your pipe back up so the pin is inside your pipe. While holding the pipe up as tight as you can over the pin retighten the set screw. You should be good as new at that point. If a shelf is in your way while trying to put the pole back in place. The shelves should have a set screw as well you can loosen enough to slide your shelves to the bottom of your cabinets. Once you got your pole in place just lift your shelves to the height you want and tighten the set screws again. Hopefully this won’t be too tough of a job for you to fix? If it’s a different kit, then I’ll have to try to figure out which one you have and go from there!

I tried to keep heavy pots and pans in mine, but they were too heavy. I now keep all my plastic ware (Tupperware) in mine and life is good again. 😁☺️

If made of wood you can buy doweling from stores like Home Depot cheaper than hardware stores to make a railing ise wood glue and also with plastic using E6000 glue. Do a dry fit nefore gluing. Good luck!