Double-stick Tape (Highest Grade Possible)
Cut out a circular piece of double-stick. Try to buy the highest quality double-stick tape that you can find since your tape may have to withstand outdoor elements: heat, humidity and possibly moisture. (Hopefully, you will be able to protect your camera if it does rain, snow, etc. since this could ruin your camera as well.)
Next, cut a piece of string long enough that you can tie it around your lens, but still be able to reach the end of your lens cap. Decide which end of the tape will stick to the lens cap itself. Now, lift the protective covering off the other end of tape, and stick your string end inside. Replace the covering. For extra protection, staple the string in several places to the tape.
After this, go ahead and tie the string to your lens. Make it tight enough so that it will stay on your lens and not slip off. If you did this right, you should now be able to have just enough string to reach the end of your lens cap. Remove the protective covering off the tape, and stick it to your lens cap.