For the nests: Heat about 4 inches of vegetable oil to 340 degrees F in a 4-quart saucepan. (Use a saucepan that is taller than it is wide.) Line a baking sheet with paper towels.
While the oil is heating, halve and rinse the leeks. Slice them thinly and put in a medium bowl. Peel the potatoes and use a mandoline to julienne them. (To julienne without a mandoline, slice the potatoes about 1/8 inch thick, stack the slices, and slice 1/8-inch thick.) Toss the potatoes, butter, flour, salt and pepper with the leeks.
Scoop about 1 cup of the potato mixture into a bird's next frying basket and immerse in the hot oil until set and golden brown. Transfer to the paper towels and repeat with the remaining mixture.
For the lobster salad: Combine the mayonnaise, mustard, lemon zest and juice, cayenne pepper, chives and tarragon in a large bowl. Season with salt and pepper. Gently fold in lobster, fennel and celery. Taste and season with more salt and pepper, if necessary
To serve, place a potato and leek nest in the centers of 4 plates. Mound a small bunch of frisee in the middle of the nests, and then top with some the lobster salad. Garnish with chives and caviar.
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