1) In a small bowl, combine sliced avocado and lemon juice. Add water to cover; set aside. Preheat an outdoor grill for high heat and lightly oil grate.
2) Heat butter in a heavy skillet over medium-high heat. Saute the onions until browned and carmelized; set aside.
3) Season the chicken with salt and pepper. Place on grill, and cook until no longer pink and juices run clear, about 5 minutes on each side. Place buns on grill just long enough to toast them.
4) Spread buns with mayonnaise to taste, then layer with chicken, carmelized onion, provolone and avocado.
Ready in 30 minutes, with cooking.