Preheat a grill for direct and indirect cooking to 425 degrees F.
Brush the pork loin all over with the olive oil and sear on all sides over the direct heat of the grill, about 15 minutes. Let cool until easy to handle, then brush the mustard on all sides of the flesh.
In a medium bowl, mix together the chili powder, cumin, garlic powder, paprika, onion powder, turmeric, salt and pepper. Sprinkle on all sides of the pork, coating evenly.
Place the pork, rib-side down, over the indirect heat of the grill. Lower the grill to 350 degrees F.
In a small bowl mix the warm water, sugar and lime juice until the sugar is dissolved. Use a brush or pour into a spray bottle to baste or spritz the pork lightly while cooking, starting 20 minutes into the cooking time and continuing every 15 minutes until done. Remove from the grill when a thermometer inserted in the center (avoiding bone) rapidly reaches 145 to 150 degrees F, about 1 hour 30 minutes total. Remove and cover lightly with aluminum foil and allow to rest 15 to 20 minutes before slicing and serving.