Gyros Burgers with Spicy Yogurt Sauce

Name: Gyros Burgers with Spicy Yogurt Sauce
Ingredients: 1/2 cup plain Greek yogurt; 1/4 teaspoon garlic powder; 1/2 teaspoon dried dill; 1 teaspoon Sriracha sauce or to taste (this amount makes a fairly spicy sauce); 1 teaspoon kosher salt divided; 1 teaspoon cumin divided; 1/2 cucumber peeled, seeded, and diced; 1 tomato seeded and diced; 1 pound ground beef; 1/2 lemon; 1/2 teaspoon dried oregano; 2 cloves garlic crushed (or substitute 1/2 tsp. garlic powder); 1/4 cup diced onion; freshly ground pepper; mixed baby greens or shredded lettuce; 4 round pita pockets