Season cavities and outside of fish with salt and pepper. Rub skin all over with coconut oil.

Thinly slice 1 lime and 1 shallot. Cut another lime into wedges and save for garnish. Fill each fish cavity with lime and shallot slices, a handful of cilantro stems (discard the rest) and the lemongrass.

Prepare the sauce: Coarsely chop the remaining shallot and juice the remaining lime. In a mini food processor, combine shallot, 1 tablespoon lime juice, the cilantro leaves, the mint, the chile, the garlic, the fish sauce and 1/4 teaspoon salt. Pulse until herbs are chopped, then add coconut milk and oil. Continue to pulse until a coarse, chunky sauce forms. (Don’t overdo it; you want a relish-like texture, not a purée.) Taste and add more salt, fish sauce and/or lime juice if necessary. (Alternatively, chop everything really finely by hand and stir in the coconut milk and lime juice.) Sauce can be prepared up to 4 hours ahead. Refrigerate until needed.

Light or heat the grill to medium-high heat. Place fish in basket and grill until blistered and just cooked through, 3 to 4 minutes per side. (Poke the fish along the spine; it should be tender but still juicy.) Serve, garnished with lime wedges and mint leaves, with sauce on the side.