To make mix, stir together the tomato juice, celery salt, Tabasco, Worcestershire sauce, lemon juice, and pepper.
Rub lemon wedge along edge of tall glass; dip edge in plate of Old Bay Seasoning. Fill the tall glass with ice and pour in vodka; top with tomato juice mix.
Add stalk of celery and lemon wedge as garnish. Place a cocktail pick through the center of a cooked, chilled lobster claw. Serve on top of drink.