It looks like a "piece" of Ascaris type roundworm, seen many of them and many have reported the same type of worm. As they digest, the ends fray and the insides degrade, so they no longer look like live worms.
It has not been proven that those in your second picture are actually from a stage of Lyme disease, so it's just as possible they are related to a stage of another parasite or even the worms. We don't know, it has not been proven just specuated.