For the chicken and pork: In a mixing bowl, whisk together the olive oil, yogurt, lemon juice, cumin, oregano, salt, Aleppo pepper, black pepper and garlic.
Place the chicken and pork into 2 separate mixing bowls. Pour half of the marinade over the chicken and the other half over the pork. Marinate, refrigerated, at least 1 hour and up to overnight.
Set up your grill for indirect heat. If using a charcoal grill, build the coals on one side only. If using a gas grill, heat one side only.
Remove the chicken and pork from the marinade, allowing excess to drain off. Keeping the chicken and pork on separate skewers, thread 4 pieces of meat onto each skewer towards the top and covering the tip of the skewer.
Place the skewers on the direct-heat side of the grill to char on all sides, about 2 minutes per side. Then move to the indirect-heat side of the grill, cover with the lid and cook until the chicken and pork are cooked through, about 10 minutes, or until the internal temperature of the chicken reaches 160 degrees F and the pork reaches 145 degrees F. Stack the skewers on a platter.
For the onions and lemons: Drizzle the onions and lemons with olive oil and season with salt and pepper. Place on the direct-heat side of the grill. Cook the lemons until charred, about 3 minutes. Cook the onions until tender, about 3 minutes per side.
Add the onions and lemons to the platter with the souvlaki. Serve with romaine, pita and tzatziki.