Place the yogurt in a cheesecloth-lined strainer or
colander, set over a bowl, and strain for 4 hours in the refrigerator to
thicken the yogurt.
Finely dice the cucumber, transfer to a colander, and
season with 1/2 teaspoon of salt. Let drain for one hour. Transfer to a
bowl and add the yogurt, garlic scapes, mint, and lime zest and juice.
Season with salt and pepper.
Prepare the burgers: Divide the lamb into six 1-inch
patties. Heat a grill pan or cast-iron skillet over medium-high heat,
and add 2 to 3 patties to the dry pan. Do not crowd the pan. Cook for 3
to 4 minutes per side for medium-rare. Remove from heat and let rest for
five minutes. Repeat with remaining patties. Serve on toasted buns with
tzatziki and a handful of baby arugula.