Thaw salmon, if frozen. Rinse and pat salmon dry. In a shallow dish combine chili sauce and soy sauce. Add salmon and turn once; set aside for 10 minutes.
Meanwhile, cook lasagna according to package directions, adding carrots the last 5 minutes. Drain. Arrange greens on a serving platter and top with lasagna and carrots; set aside.
Add salmon and marinade to a large nonstick skillet. Bring to boiling; reduce heat. Cover and cook for 8 to 10 minutes, turning once, or until salmon flakes easily when tested with a fork. Remove salmon to serving platter with greens, reserving marinade in skillet. Stir in vinegar; remove from heat. Drizzle over salmon, greens, pasta, and carrots.