I'm not a lawyer, but I would think not. Some years ago 1960s counter-culture dude Raymond Mungo wrote a memoir of his post-WWII upbringing and the crazy decade of his young adulthood, titled Famous Long Ago, taken from a well-known partial line out of Bob Dylan's song "Desolation Row". I'm sure there are other examples.
And if it's non-fiction, and you're using a lyric for scholarly, critical or parodical purposes (I don't know if you're doing any of that), there are specific provisions for such under the "fair use" provisions of U.S. copyright statutes.
caw