Make the sauce:
Peel, halve lengthwise and seed the cucumber. Coarsely shred it and in a medium bowl toss it with a pinch of salt.
Let the cucumber stand for 10 minutes and then add the yogurt, garlic, additional salt to taste; stir well.
In a large nonstick skillet heat 1 tablespoon of the oil over medium-high heat until hot.
Add the spinach and a pinch of salt and cook, stirring, for 1 minute.
Add the garlic and hot pepper flakes, if using, and cook, stirring, until all of the spinach is wilted, 1 ½ to 2 minutes.
Transfer the mixture to a shallow bowl and cool to room temperature in the refrigerator.
Wipe out and reserve the skillet.
In a food processor, process the egg until it is lightly beaten. Cut the lamb into 1-inch pieces and add it to the food processor.
Pulse 6 to 8 times or until the meat is chopped into medium-fine pieces.
Add the feta, cooled spinach mixture and ¼ cup of the bread crumbs and pulse two or three times or until just mixed.
Shape the mixture into six burgers. Spread out the remaining bread crumbs in a soup or pie plate.
Heat the remaining 2 tablespoons oil in the reserved large skillet over medium heat until hot.
Dip the burgers into the crumbs to coat them lightly on all sides; shake off any excess crumbs.
Add the burgers to the skillet and cook until golden and heated through, about 3 minutes a side.
Transfer the burgers to the pita halves and spoon some of the sauce over each burger. Garnish with the lettuce and tomatoes.
Nutritional information per serving: 331 calories; 141 calories from fat; 16 g fat (6 g saturated; 0 g trans fats); 50 mg cholesterol; 593 mg sodium; 26 g carbohydrates; 2 g fiber; 2 g sugar; 19 g protein.