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