Heat olive oil in a medium skillet over medium heat. Season the diced chicken breast with salt and black pepper. Cook the chicken until nicely browned, and the internal temperature reaches 165°F (74°C). Remove from heat and let the chicken rest for a few minutes.
Spread the herb mayo onto the tortilla and top with chicken, cucumber, tomato, capers, feta cheese, and lettuce.
Fold in the sides of each wrap, then roll it up tightly from the bottom to form a secure wrap. Cut in half.
For the homemade lemonade, mix the fresh lemon juice, water, and sugar. Stir until the sugar dissolves. Serve over ice if desired.
Serve the wrap with potato chips, pickle spears, and lemonade.