Heat up the grill to medium-high heat (or preheat your stovetop to medium-high heat).
Mix together the tzatziki sauce ingredients and set aside.
Mix together the ingredients for the cucumber salad topping and set aside as well.
Combine the ground chicken dried oregano, dried dill, garlic, feta, salt, and pepper and form the meat into hamburger patties. Brush the patties with olive oil before cooking.
Cook the burgers for 5-10 minutes on each side or until they reach an internal temperture of 165°F (If using beef or lamb then cook the burgers to your liking).
Assemble the burgers with fresh hamburger buns, greek salad topping, tzatziki sauce, and lettuce.