Place lettuce in a large bowl; drizzle with half of the remoulade sauce and season with salt and pepper. Toss until well combined. Place tomatoes in a small bowl; drizzle with olive oil. and toss to combine.
Divide lettuce evenly between 4 plates. Place avocado halves on top of lettuce and divide tomatoes evenly between each plate. Toss shrimp with remaining remoulade sauce and place on top of avocado. Garnish with scallions and serve immediately.