Cook lobster in a large pot of boiling salted water for 8 minutes, then transfer to a large bowl of ice water to let cool. Drain lobster. Remove tail and claw meat, cover, and refrigerate (save knuckle meat for another use). Put lobster shells and body into a medium pot. Add bell peppers, fennel, tomatoes, shallots, garlic, 3 sprigs of the dill, and 6 cups water. Boil over medium-high heat until stock has reduced to 2⁄3 cup, about 1 hour and 15 minutes. Strain stock into a small pot, discarding solids, and season to taste with salt. Pour half the stock into a small bowl and set aside to let cool. Sprinkle gelatin over stock in bowl and let soften for 5 minutes. Bring stock in pot to a simmer, remove pot from heat, add gelatin–stock mixture, and whisk to combine. Transfer stock to a shallow dish, cover, and refrigerate until jelled, about 4 hours.
Cook cauliflower in cream in a small pot over medium heat, stirring occasionally, until soft, about 10 minutes, then drain and purée in a blender until very smooth. Combine purée, crème fraîche, and salt and white pepper to taste in a medium bowl. Cover and refrigerate.
Preheat oven to 300°. Cut bread into 20 rounds using a 1 1⁄4" round cookie cutter. Toss rounds with butter, then spread them out on a sheet pan in a single layer. Toast in oven until evenly golden and crisp, turning once, about 10 minutes. Set aside to let cool completely.
Halve lobster tail meat lengthwise, slice tail and claw meat into 1⁄4"-thick pieces, toss with chiles, and set aside. Cut cucumber in half crosswise. Using a mandoline or a sharp knife, slice 1 of the cucumber halves lengthwise into 1⁄16"-thick strips, turning cucumber as necessary to avoid core. Set 20 of the widest strips aside, discarding remaining strips. Save remaining cucumber half for another use. Trim cucumber strips into 3⁄4" x 4 1⁄4" pieces.
To assemble the canapés, wrap 1 cucumber slice around circumference of 1 toast, pressing strip to make it adhere to itself. Spoon 1 tsp. of the cauliflower purée, then 1⁄4 tsp. of the jellied lobster stock, into the cucumber cup, top with 2 pieces lobster meat, and garnish with a frond of dill. Repeat process, making 20 canapés in all. Serve immediately.