In a bowl whisk the vinegar, lemon juice, preserved lemon, shallot, fish sauce and sugar. Whisk in ¼ cup of the oil. Stir in the chopped parsley and season with salt and pepper.
Season the salmon with salt and pepper. In a large skillet heat 2 tablespoons of the oil until shimmering. Add the salmon skin side down and sprees with a spatula to flatten. Cook until the skin is crisp. Flip the fillets and cook until the fish is cooked and flaky.
Set the salmon on plates on a few leaves of the lettuce. Drizzle on the vinaigrette. Serve and pass the remaining vinaigrette at the table.