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.
Step 2: Wrap it tightly with thread. (Cotton thread)
Wrap one end of thread around your finger. Take the other end of thread and start winding the thread around the tip, starting from about 1cm opposite to the frayed end & finish towards the tip. Try to wind it as closely & tightly as you can. The more tight you wind, the thinner the end will be. Don't worry if you leave a sopt. You can comeback and cover the missed spot. At this point glue will start to drip. Just wipe it and continue.
Step 3: Tie both ends of thread & leave it to dry.
After you finish, tie both ends of the thred. Twice. And leave it for drying for 10 minutes.
Step 4: Apply toothpaste & leave it to dry.
After it dries, it may look messy due to the glue and grime, just apply some toothpaste & leave it for drying for 5 minutes.
Step 5: Make it neat and tidy.
After it dries, just rub a brush off excess dried toothpaste & make it look even. Snip tiny bit of the tip to make it look clean.