In a food processor, combine walnuts, breadcrumbs, garlic, cumin, coriander, pepper flakes, 1 1/2 teaspoons salt, and 1/4 teaspoon pepper; process until finely ground. Add lentils and 1 tablespoon oil; pulse until coarsely chopped (some lentils should remain whole).
In a large bowl, whisk egg. Add lentil mixture; mix well. Divide into 4 equal-size parts; roll into balls, and flatten with the palm of your hand into 3/4-inch-thick patties.
Heat remaining 3 tablespoons oil in a large nonstick skillet. Add burgers; cook over medium-low heat until crisp and browned, turning gently with a thin-edged spatula, 8 to 10 minutes per side. Transfer to a paper-towel-lined plate to drain.
In a small bowl, whisk together yogurt, cilantro, and lemon; season with salt and pepper.
Assemble burgers and top with yogurt sauce, sliced red tomatoes and lettuce.