Trim celery and green onion ends; place in a pot. Add 2 tablespoons lemon juice, seafood seasoning, and blackening seasoning. Cover with water; bring to a boil.
Stir lobster tails and shrimp into the boiling water. Cook until they float to the top, about 7 minutes. Drain. Remove lobster meat from the shell; cut into bite-sized pieces. Place lobster meat and shrimp in a bowl. Refrigerate until cool.
Transfer celery and green onions to a bowl. Add seafood salad and crab dip. Drizzle remaining lemon juice on top. Mix in cooled lobster meat and shrimp. Season with a little more lemon juice.
Split and stuff croissants with lobster and shrimp salad.