Prepare an ice-water bath. Fill a large stockpot 3/4 full with cold water. Bring to a boil. Add 1/4 cup salt. Plunge lobsters head first into water. Return to a boil, and cook 10 minutes. Using tongs, transfer lobsters to ice-water bath, and let cool 5 minutes. Place lobsters on a cutting board. Working with one lobster at a time, twist tail from joint where it meets body. Cut tail in half down center. Twist claws from body; discard body. Separate claws from knuckles. Crack knuckles, and remove meat. Grasp "thumb" of claw, and bend it back to snap it off. Crack claws, and remove meat
Whisk 1/4 cup soy sauce, the cornstarch, and water in a bowl. Add lobster pieces, and toss; set aside to marinate.
Combine stock, remaining tablespoon soy sauce, the oyster sauce, mirin, lemon juice, chopped cilantro, and red-pepper flakes in a bowl.
Season beef on all sides with salt and pepper. Heat oil in a large skillet over medium-high heat. Add beef, leaving about 1 inch between each steak. Brown on all sides, about 8 minutes total. Add scallions, ginger, and garlic scapes if using. Reduce heat to medium. Cook, stirring scallions, ginger, and garlic scapes occasionally, until an instant-read thermometer inserted into beef registers 125 degrees for medium-rare, 4 to 6 minutes. Transfer steaks to a platter. Remove strings. Cover with parchment paper and then foil to keep warm.
Reduce heat to medium-low. Using a slotted spoon, add lobster pieces to sauce in skillet (reserve marinade). Cook, tossing gently, until warm, about 4 minutes. Transfer lobster to plate with beef.
Add oyster-sauce mixture and reserved marinade to sauce in skillet, and raise heat to high. Simmer, stirring occasionally, until sauce has thickened slightly, 1 to 2 minutes. Arrange beef and lobster on 4 plates. Pour sauce over top. Garnish with cilantro sprigs. Serve with rice if desired.