Looks like it's time for new boot laces. The laces I bought were too long so I had to cut. This is how I deal with the raw ends or how I repair ends that have frayed.
Method 1: Slide a short length of 1/8 inch diameter heat shrink tubing over the raw end. Gently heat with match or lighter. Snip end flush if needed. This holds up well. It works good if your lace is the fat wide type as it makes a nice round tip. The heat shrink tubing is the kind used for insulating electrical wiring connections and can be found most places that have electrical supplies.
Method 2: Saturate the tip with super glue. Snip the end if needed to remove any fraying. This hardens the lace into solid plastic and makes for easy stringing though eyelets.
Enjoy your hike. Ken