Start with the sauce so it can sit for a while. Seed and finely chop the cucumber.
In a small mixing bowl, add the cucumber, yogurt, 2 tablespoons fresh mint and season with salt and pepper to taste.
In a large mixing bowl, blend the lamb, cumin and the rest of the mint and again season with salt and pepper. Make four equally sized burgers.
Trim the tops off the pita breads so the openings are large enough to fit a burger. If you like, you can toast the pita bread or warm them up on the grill.
Cook the lamb burgers the same as you would a beef hamburger to the doneness you and your guests like.
To serve, place a burger inside a pita bread, add a slice of grilled eggplant, top with a little of the cucumber/mint sauce and finish with a little shredded romaine lettuce.