If the hat is 100% wool, you can either stitch by hand or I'd try using a glue gun. You can probably just glue the seam at the back and glue the lace to the hat at the back if you are going around the crown of the hat. If you are attaching the lace to the brim, though, then you'd better glue it all along the way. They also make permanent fabric glues that really adhere and work well. Some are water soluble and some are not.