Preheat the oven to 425 degrees . Combine 4 tablespoons of salt with the chili powder and rub over the pork tenderloins.
In a large ovenproof skillet set over medium-high heat, melt 1 tablespoon of the butter with the olive oil. Sear the tenderloins until browned, about 3 minutes on each side. Transfer the skillet to the oven and roast for 15 minutes.
Meanwhile, in a large skillet, melt the remaining 3 tablespoons of butter. Add the lima beans and cook for 5 minutes. Add the corn and apples and cook for 2 minutes more; season to taste with salt and pepper.
Remove the pork from the oven and let rest for 5 minutes before slicing. Serve the sliced pork with the succotash on the side.