Preheat a grill or griddle pan on medium heat.
Make watermelon salad: Prep the watermelon salad ingredients per instruction above. Combine all ingredients in a bowl. Season with salt and pepper to taste. Refrigerate until ready to serve.
Make marinade: In a bowl, whisk together the ingredients for the marinade. Season with salt and pepper.
Make the chicken: Set some of the marinade aside for brushing 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 use a spoon to drizzle a little more marinade over the top, once nicely marked (about 6 minutes), flip the chicken over, brush with more reserved marinade for the chicken. Close the grill (or cover pan with a lid) and cook for another 6 minutes to an internal temperature of 160°F using a thermometer. Once cooked, set aside to rest for 5 minutes.
Prep tomato and onion for sandwich per instruction above.
Brush the inside of each roll with the marinade. (Do not use the same brush as you used for the chicken.) Lightly grill or toast to golden brown.
Assemble the sandwich: Spread mayo on the inside of both halves of the bread. Layer with lettuce, tomato, chicken, cheese, and onion.
Serve: Enjoy the sandwich with watermelon salad and lemonade.