Lay four 12x12 inch squares of foil out on a flat surface. Place one chicken breast in the middle of each piece of foil.
Trim the flat end of the asparagus at 1-2 inches from the end and discard. Cut the remaining spears in half and divided them between the foil packs.
Thinly slice one of the lemons and divide the slices between the foil packs, tucking the slices in, around, and between the chicken and asparagus.
Stir together butter, garlic, juice of the remaining lemon, and Italian seasoning. Brush over chicken and asparagus. Sprinkle with salt and pepper to taste.
Fold the foil over the chicken and asparagus to close off the pack, pinch the ends together so the pack stays closed.
Grill over medium-high heat for 7-9 minutes on each side. Alternatively, bake at 200°C/fan 180°C/gas mark 6 for 15-20 minutes or until chicken is cooked through and asparagus is tender. Serve immediately.