1. To prepare salsa, combine first 6 ingredients; cover and refrigerate.
2. To prepare burgers, combine 1 1/2 cups water and lentils in a saucepan; bring to a boil. Cover, reduce heat, and simmer 25 minutes or until lentils are tender. Drain. Place half of lentils in a large bowl. Place remaining lentils in a food processor; process until smooth. Add processed lentils to whole lentils in bowl.
3. Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray. Add onion and carrot; sauté 6 minutes or until tender, stirring occasionally. Add garlic; cook 1 minute, stirring constantly. Add tomato paste, cumin, oregano, chili powder, and 1/4 teaspoon salt; cook 1 minute, stirring constantly. Add onion mixture to lentils. Add remaining 1/2 teaspoon salt, barley, and next 5 ingredients (through egg); stir well. Cover and refrigerate 1 hour or until firm.
4. Divide mixture into 8 portions, shaping each into a 1/2-inch-thick patty. Heat 1 1/2 tablespoons oil in a large nonstick skillet over medium-high heat. Add 4 patties; cook 3 minutes on each side or until browned. Repeat procedure with remaining 1 1/2 tablespoons oil and 4 patties. Serve with salsa.