Preheat your grill to medium-high heat, around 500°F (260°C).

In a large mixing bowl, combine ground turkey, pepper jack cheese, diced green chiles, cumin, garlic powder, cayenne pepper (if using), kosher salt, and black pepper. Mix gently and form into four patties.

Place the patties on a plate and chill in the freezer for 20 minutes.

In a medium bowl, mash avocado, lemon juice, lime juice, and salt until desired consistency is reached. Add cilantro if desired.

Brush grill grates with vegetable oil and grill patties for 8-10 minutes, flipping halfway through, until the internal temperature reaches 165°F (74°C) and cheese is melted.

Toast burger buns on the grill for about 1-2 minutes, then assemble by placing each patty on a bun, adding guacamole and lettuce.