Just because it's on Youtube doesn't mean it's not against the copyright yet. People break that rule all the time and it's only taken down if someone finds it and reports it.

However, I don't see the issue in working lyrics in now. If you get to the publishing stage, I'd worry about it then, personally. For now, just write.

Here is the rules about "public domain" in the U.S. currently:
"Under current U.S. copyright law work created by an individual enters the public domain on January 1, 70 years after the author's death. If the work is a joint effort of two or more authors, it enters the public domain on January 1, 70 years after the death of the last surviving author. In the case of a work made for hire, a work published under a pseudonym or a collective work, it enters the public domain on January 1, 95 years after the date of first publication or 120 years after creation, whichever occurs earlier. "