In a 6-quart slow cooker, combine the onions, chicken, lemon juice, olive oil, oregano, dill, salt, and pepper. Cover and cook on low for 4 to 6 hours, until chicken can be easily shredded with a fork. Before serving, taste and add more salt, pepper, fresh dill, or lemon juice as needed.

To make the sauce, whisk together the yogurt, lemon juice, salt, and pepper in a medium bowl. Sauce can be made ahead and kept, covered in the fridge, for up to 3 days.

To assemble the gyros, spread some of the lemon-yogurt sauce onto each piece of lavash or pita, add a few forkfuls of chicken, and top with chopped tomatoes, cucumber, onion, olives, and baby arugula. Squirt with more lemon juice if you like.