Copepods are near microscopic: you can see them with the
[hr]
eye, but you can't really make out any features, not even with a magnifying glass. Definitely not "white thin stringy threads."
Do the threads move as if they were tentacles? If so, then likely a hair or spaghetti worm: beneficial, so don't worry about them. There are many many other things that fit this bill that live on LR though. Verm. snails are another possibility.