Heat a double-burner grill pan over medium-high heat.
In a large mixing bowl, combine ground lamb, garlic, capers, parsley, zest, mustard, salt and pepper. Form mixture into 2 similar sized mounds in the bowl. Divide mixture in half, then half again. Form gently into 8 small patties.
Oil the grill pan with oiled paper towel held in tongs. Brown the burgers on the hot side of the grill for about 2 minutes on each side.
Turn heat down to medium and cook another 2 minutes for medium-rare, 3 to 4 minutes for medium.
Slice 8 mini buns in half and toast on grill or in broiler for about 30 to 60 seconds. Place on serving platter.
Top the bottom each bun with burger, slice of Roma tomato, and a spoonful of sauce. Cover with the bun top and serve.
Peel the cucumber and cut it in half lengthwise. Use a spoon to scoop out the seeds from both halves. Grate the cucumber on the wide holes of a grater, put it in a colander in a large bowl or sink and sprinkle with 1/2 tablespoon of kosher salt. Let drain for about 20 minutes. Press the cucumber with your hands to get rid of some of the moisture and place in a medium mixing bowl. Add The yogurt, dill, mint, cumin and pepper. Stir together and spoon into a serving bowl. Drizzle with olive oil.