Preheat oven to 425 F and line a baking sheet with parchment paper. Chop potatoes into 1/2 inch pieces, then toss with olive oil and salt & pepper. Roast for 30 minutes. Add broccoli to the same sheet pan and toss with olive oil and salt & pepper, roasting for the last 10 minutes of cook time.
Meanwhile, heat a large skillet over med-high heat with 1 tbsp olive oil. Mix flour, 2 tbsp lemon pepper and lemon zest together in a large bowl. Coat chicken in mixture, then add to skillet once heated through. Saute chicken for 3-4 minutes per side, seasoning generously with salt on each side, until fully cooked through.
While chicken is cooking, mix together melted butter, chicken broth, lemon juice, lemon pepper and minced garlic in a small bowl. Pour sauce overtop of chicken and add lemon slices, cooking for 1-2 minutes until sauce has thickened then remove skillet from heat.
Serve chicken with roasted potatoes and broccoli if desired, then serve and enjoy!