"Alternative lyrics" are those lyrics are written to the music of an existing song. An example would be "My Country "Tis of Thee" written to the tune of "God Save the Queen."
My understanding is that if you put the alternative lyrics to the sheet music of the original song without permission, that would be copyright infringement. (You've copied the music.)
But suppose you publish the alternative lyrics on a "standalone" basis (without the music in any form). Would the fact that it can "sing" to someone else's song be copyright infringement even if there were no "substantial similarity" in the lyrics?