Fill a large pot with 8 cups cold water. Add half the lemon juice, bay leaf, and 2 teaspoons salt. Bring to a boil.
Add shrimp and cook until bright pink and opaque throughout, 1 to 3 minutes. Transfer to a bowl of ice water to cool. Drain and pat dry. Set aside.
In a bowl, whisk together horseradish, oil, and remaining lemon juice. Season with ¼ teaspoon each salt and pepper. Add tomatoes and toss.
Divide lettuce leaves and shrimp among 4 plates. Spoon salsa on top.