Matt--Interesting photo. American ingenuity at work. These guys have done this before. The truck being loaded has a spreader mechanism on the back. Lime will fall through a gate onto the mechanism and be flung out to the sides. It seems that the spreader is driven by its own small gas engine. Simple process--no need for an expensive power take off. When loaded, no doubt it will be driven to a field, and its contents immediately spread.
The other "truck" is interesting also. Obviously repurposed from a former career, creature comforts have been completely discarded. Note the seat box. I wonder if they have somehow rigged a power take off driving a winch or if the truck is repositioned in order to raise and lower their shovel.
They will be busy for awhile. That is a lot of lime.