Bring a large pot of water to a rolling boil and generously salt the water. Add the lobster and boil for 3-5 minutes or until the lobster is cooked through.
Remove the lobster tails from the water and add to an ice bath in a large dish. Allow to sit in the ice bath for 5 minutes to cool.
Use kitchen scissors to cut the lobster shells and pull out the meat. Dice the meat into bite-sized pieces and set aside.
Add the pasta to a large bowl. Add the red onion, celery, cooked lobster, mayo, lemon juice, salt and pepper to taste. Toss well to combine and season further to taste.