Fill a large steamer or pot with about 2 inches of water. Squeeze the juice of 1 lemon into the water, then add the squeezed lemon halves and 1 tablespoon salt. Bring to a boil over medium heat.
Place the lobsters in the steamer basket or directly in the pot; cover and steam until the shells turn bright red, 8 to 10 minutes. Remove from the pot with tongs and rinse under cold water to cool slightly.
Remove the meat from the lobster shells. Roughly chop the lobster meat into 1-inch pieces. Transfer to a bowl and refrigerate 15 minutes.
Meanwhile, whisk the mayonnaise, juice of the remaining lemon, mustard and hot sauce in a medium bowl. Add the lobster, celery and any mix-ins. Toss to combine and season with salt.
Divide the lobster salad among the lettuce cups and sprinkle with the chives.