Heat oil in a saucepan over medium-low. Add red pepper, garlic, ginger, and lemongrass; cook 5 minutes. Stir in stock, honey, vinegar, and 2 1/4 teaspoons soy sauce. Bring to a simmer; cover and cook 30 minutes. Stir in black pepper.
Place tails in stock. Cover; cook 4 minutes or until a meat thermometer registers 145°. Remove tails from pan.
Split tails lengthwise. Remove meat from shells; slice. Pour cooking liquid through a sieve into a saucepan; discard solids. Keep liquid warm over low heat.
Combine remaining 1/4 teaspoon soy sauce, canola oil, and next 5 ingredients; stir with a whisk. Add pea shoots; toss.
Place about 1/3 cup cooking liquid in each of 4 shallow bowls. Arrange about 3 ounces lobster meat in each bowl; top each serving with about 1/3 cup pea shoots. Sprinkle with sesame seeds.