Take the leg of lamb out of the fridge 30 to 60 minutes before you intend to grill it. Heat a grill, or barbecue, until the temperature reaches between 450°F and 500°F.
Lightly grease the grill grate and place the lamb directly on the grill. Grill on one side for 7 to 10 minutes. Rotate the lamb half way through the cooking time if you want to create grill marks. Flip the leg lamb over and cook on the other side until it reaches an internal temperature between 130°F and 135°F.
Remove the leg of lamb onto a serving platter and tent with foil. Allow to rest for 15 to 20 minutes.
While the lamb is resting, prep the arugula salad. Toss together the baby arugula and fresh mint leaves. Squeeze the remaining half lemon over the greens and drizzle with a little olive oil. Sprinkle the salad with kosher salt and toss together.
Thinly slice the leg of lamb, making sure to cut against the grain. Arrange the lamb slices on a large serving platter and drizzle with the feta yogurt dressing. Top with the arugula mint salad and enjoy!