Preheat oven to 325°F (165°C). In a food processor, pulse the onion and garlic until finely minced. Squeeze out excess liquid.

Add the ground beef, ground lamb, oregano, cumin, salt, and pepper to the food processor. Process for 1-2 minutes until it forms a fine, tacky paste.

Press the meat mixture firmly into an 8x4 inch loaf pan, ensuring there are no air pockets. Bake for 45-60 minutes, or until the internal temperature reaches 165°F.

Remove from oven, drain the fat, and place a heavy weight (like a foil-wrapped brick or heavy cans) on top of the meatloaf. Let it cool, then refrigerate for at least 2 hours to firm up.

Make the tzatziki: Grate the cucumber and squeeze it tightly in a clean towel to remove all liquid. Mix the dry cucumber with the Greek yogurt, garlic, lemon juice, dill, and a pinch of salt. Refrigerate until ready to use.

Remove the chilled meatloaf from the pan and slice it as thinly as possible (1/8 inch thick).

Heat a small amount of oil in a skillet over medium-high heat. Pan-fry the meat slices for 1-2 minutes per side until browned and crispy.

Warm the pitas. Assemble by spreading tzatziki on the pita, topping with crispy meat, lettuce, tomatoes, cucumbers, and red onions. Fold and serve immediately.