Should I take humaworm while on lyme antibiotics? No, absolutely not. Finish the prescribed antibiotics first, then do Humaworm.
A note: antibiotics, as well as Humaworm, will also kill any good bacteria residing in your digestive tract. You may want to give yourself a brake in between the two treatments, in order to give your digestive system a chance to recuperate before you go after it again with blazing guns. :-) The brake I have in mind would be something like 2 weeks or so.