For the tzatziki, wash cucumber (peel if desired) and cut in half lengthwise. Slice thinly.
In a medium bowl, combine cucumber, yogurt, lemon juice, garlic, dill and salt and pepper. Stir until well combined and set aside.
For the lamb rolls, preheat gas or charcoal grill to medium.
Wash and trim eggplant and cut lengthwise into ¼ inch slices. (You can salt the eggplant to remove some moisture if you like, but I find it makes little difference when grilling the eggplant).
Grill eggplant slices until tender and slightly charred, about 4 minutes per side. Remove from grill and transfer to a large bowl. Toss with 1 tablespoon oil, salt and pepper and tent with foil to keep warm.
In a large skillet over medium high heat, heat remaining oil until shimmering but not smoking. Add onion and saute until translucent, about 5 minutes.
Add lamb, marjoram, salt and pepper and cook until lamb is cooked through and no longer pink, about 10 minutes.
To serve, lie two or three eggplant slices on each plate. Spoon lamb mixture onto center of eggplant slices and sprinkle with feta. Roll eggplant carefully around filling and turn so seam is on bottom.