Whisk broth, remaining 1 1/2 tablespoons molasses, 1 1/2 tablespoons lime juice and oil in a 10-by-14-inch roasting pan. Add onions, sweet potatoes, okra and thyme; season with salt and pepper to taste and toss well. Cover tightly with foil.
Bake the vegetables until sweet potatoes begin to soften, 25 to 30 minutes.
Push the vegetables to sides of the pan. Place the pork in center and pour any remaining marinade over it. Roast, uncovered, until just a trace of pink remains in the center and an instant-read thermometer inserted in the thickest part registers 155°F, 30 to 35 minutes. Transfer the pork to a cutting board and let rest for 5 minutes. Slice thinly on the diagonal. Serve with the vegetables.
TIPS & NOTES Make Ahead Tip: The pork can be marinated overnight.