Melt butter over medium-low heat; skim solids off top, and discard. Pour remaining butter into a bowl, leaving any solids in pan; discard solids. Stir in tarragon, parsley, and chives; season with kosher salt. Set aside.
Carefully position a knife on top of each lobster's head between the eyes, and draw it sharply through the head to kill it instantly. Place lobsters, belly up, on a cutting board, and cut each lobster in half. (Lobsters may also be parboiled and then split before grilling.)
Preheat grill to medium-high heat (350° to 400°). Drizzle lobster halves with olive oil, and season with kosher salt and pepper. Grill lobster halves, shell sides down, basting with 1/4 cup herb butter several times, 7 minutes or until meat is opaque. Serve lobsters with lemon wedges and remaining herb butter.