Preheat the oven to 425 degrees F (220 degrees C). Line a rimmed baking sheet with parchment paper.
Whisk together onion, feta cheese, bread crumbs, eggs, parsley, garlic, oregano, and lemon zest in a large bowl. Add turkey, salt, and pepper; mix until well combined.
Use wet hands to form mixture into twenty 1 ½- to 2-inch meatballs. Transfer to the prepared baking sheet.
Bake in the preheated oven until browned and slightly firm, 10 to 12 minutes; meatballs will not be fully cooked at this point. Let meatballs cool completely, about 20 minutes.
Combine cooled meatballs and green beans in a large, resealable freezer bag. Tightly seal the bag, allowing as much air to escape as possible. Freeze for up to one month.
When ready to cook, preheat the oven to 425 degrees F (220 degrees C). Line a rimmed baking sheet with parchment paper.
Empty frozen meatballs and beans onto a large, rimmed baking sheet. Add cherry tomatoes and toss with olive oil, salt, and pepper.
Bake in the preheated 425 degree F (220 degree C) oven until veggies are tender and meatballs are cooked through, about 20 minutes.
Meanwhile, stir together Greek yogurt, lemon juice, lemon zest, dill, and salt for tzatziki sauce.
Serve meatballs and veggies with pita rounds and tzatziki sauce.