Heat your oven: To 350°F (175°C).
Prepare your leeks: Trim the root ends and peel back layers until no visible dirt remains. Rinse thoroughly and slice into 1-inch rings.
In a large ovenproof pan, heat a couple tablespoons of olive oil over medium-high heat. Add leek slices, season with salt and pepper, and cook until browned, about 4 to 5 minutes per side.
Sprinkle pan with sliced garlic, then add dried lentils. Pour in broth, using it to rinse lentils off the tops of leeks. Scatter with lemon zest and scallions, and season as needed.
Bring to a simmer, cover, and transfer to the oven. Cook for 40 to 45 minutes, or until leeks are soft and lentils are tender.
While the leeks and lentils cook, combine yogurt with 1 tablespoon lemon juice, 1 minced garlic clove, and salt and pepper to taste.
In a large bowl, whisk 2 tablespoons lemon juice with 3 to 4 tablespoons olive oil and season with salt and pepper. Toss arugula with dressing.
Take the braised leeks and lentils out of the oven. Serve by dolloping with yogurt sauce and scattering arugula on top, or arrange on a plate.
