Prepare the salmon: Whisk the grapeseed oil, ginger, garlic, shallot, lemongrass, lime juice, fish sauce, brown sugar, a pinch of salt and 1/2 cup water in a medium bowl. Place the salmon on a rimmed baking sheet and pour the marinade on top. Turn the salmon so the marinade coats both sides. Cover and refrigerate, 30 minutes.
Meanwhile, make the carrot-sesame dressing: Whisk the fish sauce, rice vinegar, Sriracha, sesame oil, brown sugar, lime juice and a pinch of salt in a medium bowl until the sugar dissolves. Add the carrot, scallions and 1/4 cup water; stir to combine. Set aside.
Preheat a grill to medium high. Remove the salmon from the marinade, wiping off any excess. Brush the grill grates with grapeseed oil. Brush the skin side of the salmon generously with grapeseed oil, then place on the grill skin-side down. Cover and cook until the skin is crisp and the salmon is nearly cooked through, about 8 minutes. Uncover and cook until the salmon is just cooked through, about 5 more minutes. (Do not flip the fish.)
Transfer the salmon to a platter and spoon the carrot-sesame dressing on top.