Heat olive oil in a medium skillet over medium heat. Season the diced chicken breast with salt and black pepper. Cook the chicken, stirring occasionally, until browned and the internal temperature reaches 160°F (71°C). Remove from heat and let rest for a few minutes.
Spread the herb mayo onto each tortilla. Evenly distribute the cooked chicken, cucumber, tomato, capers, feta cheese, and romaine lettuce over the tortillas.
Fold in the sides of each tortilla, then roll it up tightly from the bottom to form a secure wrap. Slice in half.
For the homemade lemonade, mix the fresh lemon juice, water, and sugar. Stir until the sugar is fully dissolved. Serve over ice if desired.
Serve the wraps with potato chips, pickle spears, and a glass of lemonade.