Preheat the broiler. Place the bell peppers on a baking sheet and broil, turning every 5 minutes, until charred all over, about 20 minutes. Transfer to a bowl and cover; let sit for 10 minutes. Using your fingers, peel and discard the charred skin. Discard the stems and seeds.
Meanwhile, grease a baking sheet with 1 tablespoon olive oil. In a large pot of boiling, salted water, cook the lasagna noodles until al dente. Drain and rinse with cold water. Arrange in a single layer on the prepared baking sheet to prevent sticking.
In a medium bowl, combine the tuna, dill, lemon juice and 1/4 cup olive oil; season with salt and pepper.
Using a blender, puree the roasted peppers, sherry vinegar and 1/2 teaspoon salt. With the machine on, pour in the remaining 5 tablespoons olive oil in a slow stream, blending until thick, about 30 seconds.
Place a layer of lasagna noodles in the bottom of a 9-by-13-inch baking dish. Top with one-third of the arugula and one-quarter of the bell pepper sauce. Repeat 2 more times, using the remaining tuna mixture and arugula and topping with the remaining noodles. Divide the lasagna into 6 portions. Top with the remaining red pepper sauce and the chives.