Preheat a grill or griddle to medium heat.
Grill the chicken breasts 5–6 minutes per side, until the internal temperature reaches 165°F (74°C); remove and let rest.
While the chicken cooks, whisk together lemon juice, olive oil, Worcestershire sauce, Greek yogurt, chopped garlic, salt, pepper, and oregano in a small bowl to make the dressing.
Dice the rested chicken into bite-sized pieces and transfer to a large bowl.
Toss the warm chicken with half of the dressing to coat, then add the chopped lettuce and croutons and pour in the remaining dressing; toss to combine.
Divide the salad mixture among the tortillas, sprinkle with the Parmesan, roll each tortilla tightly, and slice in half to serve.
