Combine flour and cayenne pepper in a large resealable plastic bag. Add a few chicken strips at a time and shake to coat.

Melt butter in a large, nonstick skillet over medium heat. Add chicken and cook until browned on all sides, 4 to 6 minutes.

Combine lime juice, honey, brown sugar, and Worcestershire sauce in a bowl; pour over the chicken. Continue to cook until juices run clear and the sauce is thickened, 3 to 5 more minutes.