Put the pork on a platter and sprinkle all over with salt and pepper.
Add the olive oil and lime juice and turn to coat the pork with the marinade. Cover with plastic wrap and set aside in the refrigerator.
For the Chile-Coconut Sauce:
Heat the olive oil in a saucepan over medium heat. Add the ginger, garlic, lemongrass and chile and cook to soften, about 3 minutes. Add the coconut milk, and sugar and simmer until thickened, about 5 minutes. Stir in the lime juice and season with fish sauce, and salt and pepper. Cool to room temperature. Add cilantro stems and puree using an immersion blender or food processor.
Preheat an outdoor gas or charcoal grill. Blot some oil onto a thick square of paper towels, and then carefully and quickly wipe the hot grates of the grill to make a non-stick surface. Put the pork on the grill and cook, turning to brown all sides, until crusty on the outside and almost cooked through but still slightly pink in the center, 10 to 15 minutes.
Remove from the grill and let rest for a few minutes.
To serve, slice the pork and add it to the bowl with the tomato salad. Pour over the chile-coconut sauce and toss it all together.