Combine 1 1/2 cuts water and lentils in a saucepan; bring to a boil. Cover, reduce heat, and simmer 25 minutes or until 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.
Heat a large nonstick skillet over medium-high heat.Coat pan with cooking spray. Add onion and carrot; saute 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.
Divide mixture into 6 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 3 patties; cook 3 minutes on each side or until browned. Repeat procedure with remaining 1 1/2 tablespoons oil and 3 patties. Serve with a spicy fruit salsa or we've enjoyed them as a regular burger in a bun and with cheese.