Bring a large stockpot of water to a rolling boil, add lobsters, and cook at a fast boil until done, about 10 minutes. Transfer to a bowl of iced water to cool, then remove and reserve tail and claw meat for another use. Do this messy job over a bowl to reserve drippings. Crush shells, which will be the base for the stock, using a mallet or hammer, then grind as fine as possible with reserved drippings in a food processor.

Melt butter and oil in a large stockpot over medium-high heat. Cook onions, carrots, celery, and salt until golden, about 10 minutes. Stir in crushed shells, white wine, and Madeira. Turn heat to high and cook until liquid is reduced by half.

Add clam juice and tomato juice. Bring to a boil and carefully skim and discard foam that rises to surface. Add remaining ingredients and cook at a simmer, uncovered, 1 hour 15 minutes.

Strain through a fine sieve and refrigerate up to 2 days or freeze indefinitely.