Preheat oven to 425F. Grease a baking sheet and set aside.
In a large bowl, gently mix together the ground beef, egg, breadcrumbs, red onion, garlic, salt, pepper, oregano, cumin, marjoram, red pepper flakes, parsley and dill until evenly combined. Optional: You can wrap this in plastic and chill for a few hours or overnight to marinate and deepen the flavor. If you don't have the time, you can just use it right away with no problem. Shape into meatballs and place on baking sheet. Bake until golden and crispy, 20 to 25 minutes.
In the meantime, to make the tzatziki, in a small bowl, stir together the yogurt, cucumber, lemon juice, parsley, dill, garlic, oregano, red pepper and a large pinch of salt and black pepper. Cover with plastic wrap or store in an airtight container until ready to use. You can make this a couple days ahead of time and keep it in the fridge for up to a week.
To assemble the gyros, slice the meatballs in half, warm the pita breads and gather the rest of the toppings. Top each warm pita with tzatziki, lettuce, a few meatball halves, more tzatziki, tomatoes, cucumber, red onion, dill and parsley. Roll up and serve immediately or at room temperature. Enjoy!