In a medium mixing bowl combine the goat cheese with the lemon juice, salt, pepper, and basil; mix together well and set aside. Cut the phyllo pastry in half lengthwise so that you have 2 (5 1/2-inch) wide pieces of dough. Keeping the piles of dough covered with a damp tea towel, lay one sheet of phyllo out on a lightly floured surface, brush it with a little melted butter, and place another sheet on top of it, staggered bu 1/2-inch to the left. Repeat until you have 4 layers of phyllo, staggering each by 1/2-inch, and then repeat the process to make a second identical pile. Spread half the goat cheese mixture in a line 1/2-inch in from one long inner edge of each phyllo pile. Next to the strip on the inside, make a long line of half the shredded crab meat. Distribute half the grilled onions and asparagus next to the crab, brush the long edge and the 2 short edges of the phyllo with meted butter and roll up the strudels tightly from left to right, squeezing the edges to seal them. Place the 2 strudels seam-side down on a baking sheet and brush the outside of each strudel with more melted butter. Sprinkle with the bread crumbs and, if desired, refrigerate for up to 2 hours.
Roast the bell peppers over a gas flame, or on a tray under a hot broiler, turning so that the skin is evenly charred without burning and drying out the flesh. transfer the charred peppers to a plastic bag, tie the top closed and let steam until cool to the touch, about 15 minutes. The easiest way to peel them is to pull off the charred skin by hand and then dip the peppers briefly in water to remove any blackened bits. Do not peel them under running water since that will wash away flavorful juices. Once peeled, cut away stems, seeds, and veins. In a blender, process the flesh to a smooth puree. You should have about 1 cup of puree.
In a medium mixing bowl, combine red pepper puree with the lime juice, sour cream, paprika, salt, and pepper to taste. Blend together well and refrigerate, covered, until needed.
Preheat the oven to 400 degrees and bring the sauce to room temperature. Bake the strudels in the hot oven for about 15 to 20 minutes, or until they are crisp and golden. Remove them to a cutting board, rest for 5 minutes, and slice off and discard or eat the very ends of the strudels. Slice each strudel into 3 equal lengths and slice each length into 3 spirals. Make a little pool of the red pepper sauce on each of 6 plates and place 3 spirals, cut side up, on the sauce. Garnish with a leaf of lettuce and serve immediately.