Fill a small pot with water and squeeze lemon juice and add lemon halves themselves into the pot. Bring pot to a boil. Add lobster tails lower heat to medium-low and poach tails for 9 to 12 minutes. Remove tails from liquid and reserve ½ cup of the lobster stock. Remove the lobster meat from the shells and set aside.
In a large saucepan heat oil over medium-high heat. Place lobster shells (including poached tail shells) into the pan and sauté for 3 to 4 minutes. Add tomato paste and toss together until the shells are well coated. Continue to sauté for 2 to 3 minutes.
Add the carrots, celery, onion, garlic, and herbs and continue to sauté for 4 to 5 minutes or until onions become slightly translucent. Season with salt and pepper.
Deglaze pan with brandy and sherry and stir.
Continue to cook mixture until most of the liquid has evaporated. Add poaching liquid and stock/clam juice and reduce heat to medium. Simmer for 10 to 12 minutes.
Pour entire contents into a blender and puree for 2 to 3 minutes.
Strain mixture back into the saucepan, using a fine-mesh sieve. Place pan back over medium heat and simmer.
In a small bowl mix together butter and flour. Whisk butter-flour mixture into the bisque and continue to stir until mixture slightly thickens.
Stir in the cream and adjust seasonings.
Chop reserved lobster tail meat into bite-sized pieces. Divide lobster meat into two soup bowls and top with a ladle or two of lobster bisque. Finish with minced tarragon and cracked black pepper. Serve with a crusty baguette.