Bring 4 quarts water and salt to a boil in a large stockpot. Plunge lobsters, head first, into boiling water; return to a boil. Cover, reduce heat, and simmer 10 minutes; drain and cool.
Remove meat from claws and tails. Chill lobster meat.
Cook asparagus in boiling water to cover 3 minutes or until crisp-tender; drain. Plunge into ice water to stop the cooking process; drain and pat dry. Set aside.
Combine olive oil through pepper in a jar; cover tightly, and shake vigorously.
Arrange lettuce leaves, lobster, and asparagus on plates; drizzle with dressing; add tarragon sprig and lemon wedge to each serving, if desired.
