How to Make It
Light a grill or preheat a grill pan. In a large bowl, whisk the lime juice, fish sauce, water, sugar and garlic until the sugar dissolves. Stir in the shredded carrot and set aside.
Brush the romaine hearts with canola oil and season lightly with salt and pepper. Grill cut side down over high heat until lightly charred on the bottom, 1 to 2 minutes. Turn the romaine and grill until it just starts to wilt, 1 to 2 minutes longer. Transfer the romaine to a plate or bowl and cover loosely with plastic wrap to steam. Let cool slightly, then cut the hearts into bite-size pieces. Add the romaine to the dressing in the large bowl and toss well.
Oil the grill grate. Brush the swordfish steaks with canola oil and season with salt and pepper. Rub each steak all over with 1 1/2 teaspoons of the onion soup mix. Grill the swordfish over moderately high heat, turning once, until the fish is lightly charred on the outside and just cooked through, 4 to 6 minutes. Transfer the grilled romaine salad and swordfish to plates. Garnish with chopped cilantro and mint and serve.