Mix all ingredients and spices (for either souvlaki or gyros) in a large non-metallic bowl with a good drizzle of olive oil.
Split your chicken thighs into 2 equal pieces for the chicken souvlaki and/or slice your lamb shoulder into ½” thick slices.
Using a meat tenderizing mallet or rolling pin, flatten your pieces of protein to around ¼” thick by placing between a folded piece of cling wrap first.
Add your meat to your spice mix in a large non-metallic bowl, and mix to coat well. Refrigerate overnight, or for a minimum of 4 hours.
When ready to cook, light your BBQ using a chimney starter and charcoal briquettes, and add lump charcoal.
While your BBQ is coming up to temp, thread your meat onto your rotisserie rod, overlapping each piece, and bookending with half an onion. Press down to keep compact, and tighten all prongs onto the rod.
Put your rotisserie rod over the lit charcoal (which should be to the sides and not directly underneath), and keep topped up with charcoal during the cook. This should take around 2.5 hours, cook to internal temp of around 170°F for chicken and 155-160°F for lamb.
Whilst your protein is cooking, prepare the salad by chopping tomato and cucumber into ⅓” pieces, and thinly slicing the red onion, and mix together with olive oil and a squeeze of lemon juice and dried mint. Add feta (optional) and salt and pepper to taste.
Make your tzatziki also by combining all ingredients in a medium bowl, then cover and refrigerate.
In the last few mins of cooking, split a pita in half and warm on a grill over the coals.
When your protein is at the desired internal temp, take the rod off the heat and slice directly from the rod.
Stuff your pita with your sliced pieces of meat, and top with salad and tzatziki sauce.
Enjoy with family and a cold beer!