How to use Heat Shrink Tubing
Whip the ends of your lacing a couple of times using thread and needle, leave the needle attatched; pass this through your section of tubing and then roll the tubing (carefully) next to a candle flame or over steam.
Once the tubing has shrunk into place allow to cool and trim the end.
The tips will not be as hard as shoe lace ends but will be rigid enough to prevent fraying and allow the lace to be threaded through eyelets easily.