Well it's common for an automotive drum brake to do what you are referring to. But you usually only hear it when you step on and release the brake pedal at really low speeds.
But the automotive brake shoe has three pads that rub on the backing plate, where trailer shoes do not seem to have these pads.
I would pull a wheel and pull the shoes. Clean the backing plate off really well with a garden hose and a small scrub brush. Now inspect the backing plate for wear or grooves from the shoes. Sand any grooves smooth and put it all back together.
If you want to lube it I would look for some brake caliper lube.
LinkUse it sparingly though so it doesn't wind up on the shoes.