Bring broth and 1 1/2 cups water to a boil in a saucepan. Add lobster; cover and cook for 4 minutes. Remove lobster from pan; cool for 5 minutes. Remove meat from cooked lobster tails, reserving shells. Chop meat.
Place shells in a large zip-top plastic bag. Coarsely crush shells using a meat mallet or heavy skillet. Return crushed shells to the broth mixture. Reduce heat to medium-low. Cover and cook for 20 minutes. Strain shell mixture through a sieve over a bowl, reserving broth; discard solids. Return broth mixture to saucepan; keep warm over low heat.
Heat 1 tablespoon butter in a medium saucepan over medium-high heat. Add rice to pan; cook 2 minutes, stirring constantly. Stir in 1 cup broth mixture, and cook for 5 minutes or until liquid is nearly absorbed, stirring constantly.
Reserve 2 tablespoons broth mixture. Add the remaining broth mixture, 1/2 cup at a time, stirring constantly until each portion is absorbed before adding the next (about 22 minutes total). Remove from heat, and stir in lobster, the reserved 2 tablespoons broth mixture, 2 tablespoons butter, and green peas.