OK, there are probably more than 10 different ways to repair frayed laces due to wear and tear. This is just another way. In my opinion most simplest & quickest method that I could think of using minimal requirements. Just two actually. (well If you skip the glue, just one.)
So you need
1. Thread (Preferably cotton, as it soaks in lot of glue and grips better)
2. Any glue used for crafts, leather repair, furniture repair will do But NOT superglue! I used craft glue 'Fevicol'
3. Toothpaste (Optional)
Step 1: Apply some glue on the frayed end.
Dab the frayed end on tiny amout of glue. Take in the glue like a paintbrush.