Put lentils in a large pot with enough water to cover by 2 inches; bring to a boil and cook until tender, about 20 minutes. Transfer lentils to a large bowl.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Saute onion, bell pepper, and celery in hot oil until onion is slightly browned, 5 to 7 minutes; add to lentils and stir.
Stir rice, 1 cup tahini, mustard, lemon juice, parsley, and lemon juice into the lentil mixture; shape into patties.
Spread bread crumbs into a wide, shallow bowl. Press patties into the bread crumbs to coat.
Heat 1/4 cup olive oil in a saucepan over medium-high heat. saute garlic in olive oil until fragrant, 1 to 2 minutes. Stir cumin into the oil and remove pan from heat; add water, 1 cup tahini, and lemon juice and stir until smooth. Season sauce with salt.
Heat a large skillet over medium heat. Cook patties in hot skillet until beginning to crisp, 7 to 10 minutes per side. Drizzle sauce over patties to serve.