Heat oven to 425°F and line a rimmed sheet pan with parchment paper.
Place the chicken breasts on the sheet pan and season with salt and pepper. Slather with about 3/4 of the bottle of LEMON BUTTER SAUCE. Roast the chicken until the internal temperature reaches 165°F, 20-25 minutes. Remove from the oven and let rest for 10 minutes. Slice into thin slices, tossing with any juices and sauce that accumulate on the sheet pan. Set aside.
To make the dressing, whisk together the mustard, mayonnaise, 1 Tbsp of the LEMON BUTTER SAUCE, the feta, the olive oil and the lemon juice. Season with salt and pepper. Toss half of the dressing with the romaine lettuce. Be sure to do this right before assembling the wraps.
Lay a wrap out on a clean surface. Set 1/6th of the chicken horizontally in the center of the wrap, leaving about 1-inch on each side. Drizzle the chicken with a bit of the remaining dressing, then top with 1/6th of the avocado, cilantro, then greens. Repeat with remaining ingredients.
Fold the left and right side over the filling, then lift the bottom up and over the filling, tucking in the edges, and rolling away from you to create a burrito-like package. Flatten the wrap a little with the palm of your hand.
Brush each long, flat side with butter. Heat a cast iron grill (or a BBQ) over medium-high heat. Grill each side until a little crispy, and browned. Slice in half and serve with hot sauce.