Remove about 4 cups (1 quart) of the Seafood Bouillon and chill to use for an ice bath.
Bring the remaining Seafood Bouillon back to a boil in a large stockpot. Preheat a grill to medium-high heat.
Put the reserved chilled Seafood Bouillon in a large bowl and add ice to make an ice bath. Add the lobsters to the boiling liquid in the stockpot and cook for 2 minutes. Remove the lobsters from the pot. Remove the claws and return them to the stockpot to cook for 6 minutes more. Put the lobster bodies in the ice bath to stop the cooking process. When the claws are cooked, transfer them to the ice bath to chill. Use a chef's knife to split the lobster bodies and tails in half down the center. Crack the claws and remove the meat.
Melt half of the Pernod-Caper Butter in a small saucepan on the grill. Brush the lobster tails liberally with some of the remaining room-temperature Pernod-Caper Butter. Grill the lobsters on the shell side first for 4 minutes to melt the butter. Flip onto the flesh side, add the claw meat to the grill and cook for another 4 minutes. Remove to a platter or individual serving plates.
Serve with a salad of shaved radishes and fennel, lemon wedges for squeezing and a small side of the melted Pernod-Caper Butter.
Combine the salt, lemons, carrots, celery, onions, bay leaf and 24 cups (1 1/2 gallons) water in a large stockpot and bring to a boil. Use immediately for cooking lobsters or other seafood.
Combine the butter, shallots, capers, dill and lemon zest in the bowl of a stand mixer fitted with a paddle attachment and mix on medium just until the ingredients are combined. Scrape down the sides of the bowl with a spatula, then add the Pernod and mix on high just until incorporated. Season the butter with salt and pepper.
Using a sheet of parchment paper, roll the butter into a log, seal the ends and chill for at least 1 hour. When ready to use, slice into disks for easy portioning.