Peel and shred half of an english cucumber. Take the shredded bits and squeeze out any excess water thoroughly with a cheesecloth or coffee strainer.
Add Greek yogurt, shredded cucumber, minced garlic, lemon juice, dill, mint, and olive oil to a large bowl. Combine until well mixed and season with salt and pepper to taste. Allow the Tzatziki sauce to refrigerate for at least three hours.
Peel the onions and garlic and blend them in a food processor until well minced. Again, take it out and squeeze out any excess liquid.
Add the ground lamb, ground beef, onion, garlic, rosemary, thyme, salt, and pepper to the food processor and blend until the meat is very smooth.
In a lightly greased loaf pan, spread the meat mixture out and pat it down to remove any extra spaces.
Bake the gyro meat in an oven set to 325°F for 45 minutes to an hour.
Remove the meat and refrigerate it to make slicing easier.
Once the meat has been chilled for a few hours, thinly slice it and sear both sides in a hot skillet.
Add the meat to a pita with tzatziki sauce, lettuce, tomato, red onion, and top it off with feta cheese crumbles.