Place onion, parsley, garlic, lemon juice and zest, black pepper, salt, za’atar and olive oil in food processor and blend until smooth.
Pour the marinade over the lamb and veggies and mix well to ensure everything is coated.
Cover and refrigerate for up to 3 hours (If time is tight, marinate at room temperature for about 30 minutes).
Assemble the kabobs by threading a piece of lamb, alternating with veggies, leaving space between the pieces for air circulation to cook evenly.
Brush grill or grill pan with oil and heat to medium high.
Place kabobs on grill, rotating each one-quarter turn every couple of minutes, until the meat is completely browned, from 7 to 10 minutes, depending on how well-done you prefer your lamb.