Finely mince the mint and parsley, and peel and chop the onion.
In a large bowl, combine the ground lamb, chopped onion, 4 tablespoons each of the mint and parsley, 1 teaspoon cumin, 1/2 teaspoon cinnamon, 1/2 teaspoon salt, and a pinch of cayenne pepper. Mix well using your hands until everything is evenly combined, and form the mixture into burger patties. Set aside.
To make the sauce, combine Greek yogurt, the remaining 1 tablespoon each of mint and parsley, remaining 1/4 teaspoon cumin, and a pinch of salt and cayenne pepper, as desired. If you prefer a thinner sauce, add 1-2 teaspoons olive oil. Stir well and keep in the fridge while you cook the burgers and prep the salad.
Cook the lamb burgers on an oiled grill rack or in a heavy frying pan over medium-high heat, for about 5 minutes on each side, until they reach an internal temperature of 160F.
While burgers cook, prep the salad. Combine halved cherry tomatoes, sliced cucumber, olive oil, and red wine vinegar in a small bowl. Sprinkle feta on top.
Serve burgers warm with the salad, yogurt sauce, and pita bread, as desired. Enjoy!
Notes
You can also use a spoon or spatula to make the lamb mixture, but it will take longer and probably mix less evenly. I find it worthwhile just to deal with it and wash my hands very well afterward.
1 1/2 pounds of lamb makes 4 medium-sized burgers. If you're feeding 2 or 3 people, you could just use 1 pound of meat, and use a scant amount of each herb and spice in the meat mixture. No need to be too exact.
The same meat mixture works well as meatballs. Form 1-2 tablespoons of the mixture at a time into balls, and cook on the stove top, or wrap in foil and cook on the grill.