Whisk 2 tablespoons oil with 1 tablespoon lemon juice until combined.
Combine shrimp with remaining 2 tablespoons lemon juice, the salt, and pepper, and let stand for 10 minutes.
Heat remaining 2 tablespoons oil in a skillet over high heat. Add shrimp and juices, and cook, stirring, until shrimp are pink and cooked through, 1 to 2 minutes. Transfer shrimp and juices to a bowl.
Add endives, avocados, tarragon, and dressing to shrimp, and gently toss. Serve immediately.