In a large gallon size zip-top bag, combine the ingredients for the lamb and toss to combine. Seal and chill at least 1 hour or up to 12 hours.
Meanwhile, preheat the oven to 425 degrees F.
Place the potatoes on a large baking sheet and drizzle with olive oil, salt + pepper. Gently toss with your hands or two spatulas to evenly coat. Bake for 15-20 minutes, then flip and bake for 15-20 minutes more. During the last 5 minutes of cooking, add the oregano and toss well. You want the potatoes to be tender, but crisp on the outside.
Set your grill, grill pan or skillet to medium-high heat. Thread lamb pieces onto skewers. Discard marinade.
Grill lamb until lightly charred and cooked to your liking, turning skewers occasionally throughout cooking, about 8 to 10 minutes total. Cooking time will vary depending on the thickness of your lamb and your desired doneness. Transfer skewers to plate.
To assemble the plates, add a couple lamb skewers and potatoes to each plate. Serve with cucumbers, pickled red onions, feta cheese, hummus and avocado tzatziki (recipe below). EAT!