Combine 2 cups water, carrots, lentils and 1/4 teaspoon salt in a saucepan.
Bring to a boil.
Reduce heat to low.
Partially cover and simmer until the lentils are tender and falling apart, 12 to 14 minutes.
Drain in a colander, gently pressing out excess liquid.
Transfer to a plate; let cool to room temperature, about 20 minutes.
Meanwhile, toast cashews in a small dry skillet over medium-low heat, stirring, until golden and fragrant, 2 to 4 minutes.
Transfer to a plate to cool.
Heat 2 teaspoons oil in a large nonstick skillet over medium heat.
Add onion and cook, stirring, until softened, 5 to 8 minutes.
Add garlic, curry powder and the remaining 2 tablespoons water; cook, stirring, for 1 minute.
Remove from heat and let cool.
Prepare Cucumber-Mint Raita, if using.
Pulse the cashews in a food processor until finely chopped.
Add the lentils and the onion mixture; pulse until the mixture is cohesive but still somewhat textured.
Transfer to a bowl and stir in breadcrumbs, the remaining 1/2 teaspoon salt and pepper; mix well.
With dampened hands, form the mixture into six 1/2-inch-thick patties, using about 1/2 cup for each.
Using 2 teaspoons oil per batch, cook 2 to 4 patties at a time in a large nonstick skillet over medium heat until evenly browned and heated through, about 4 minutes per side.
Cut small ends off pitas and open the pockets.
Serve burgers in pitas, with lettuce, cucumber and the raita, if desired.