Preheat a grill or griddle pan on medium heat.

In a bowl whisk together the ingredients for the marinade. Season with salt and pepper. (Marinade should taste good on its own; adjust the seasonings to taste.) (Set about half of the marinade aside to brush on each bun.)

Make the chicken: Brush the chicken with the marinade on one side and season with salt and pepper.

Place the brushed side of the chicken on the grill or griddle pan, then brush more marinade over the top; once nicely marked (about 6 minutes), flip the chicken over, and brush with reserved marinade for the chicken. Close the grill (or cover the pan with a lid) and cook for another 6 minutes to an internal temperature of 160°F (71°C) using a thermometer. Once cooked, set aside to rest for 5 minutes.

Brush the inside of each bun with the marinade. Lightly grill or toast to a golden brown. Then set aside.

Make the sandwich: Spread mayo on the inside of both halves of the bread. Layer with lettuce, tomato, chicken, cheese, and onion.

Mix the ingredients for the homemade lemonade.

Serve the Greek grilled chicken sandwiches with pita chips and hummus and a glass of lemonade, over ice if desired.