Infuse the cucumber water: Place the cucumber slices in cold water and refrigerate until ready to serve, at least 15 minutes.
Cook the rice: Prepare the rice according to package instructions. Once tender, fluff the rice with a fork and season with salt and pepper to taste.
Heat extra-virgin olive oil in a pot over medium-high heat. Brown the lamb on all sides. Add leeks, scallions, celery and garlic to the pot and sauté until softened.
Pour in chicken broth to cover the mixture. Season with salt and pepper. Cover and simmer for 30–40 minutes. Then stir in the spinach and dill.
Stir in spinach and dill and simmer until the lamb is fork-tender and only about ¾ cup of liquid remains in the pot. Turn off heat.
Make the sauce: In a small bowl, whisk the egg with cornstarch and lemon juice until frothy.
Temper the sauce: While whisking the egg, slowly pour a ladle of broth from the pot into the egg mixture to temper. Then stir the mixture back into the pot, stirring gently to combine. Gently simmer until the sauce thickens. Then remove from the heat.
Whisk the ingredients for the dressing.
Make the salad: Mix the tomatoes, cucumber, onion, olives, feta. Toss with the dressing.
Optional: warm the pita in a pan over medium heat on both sides until soft and pliable. Cut into wedges.
Serve the lamb fricassée garnished with chopped dill with rice, pita, village salad, and cucumber water.