I think you have this line wrong; it should be "Lay down your reeds, and run for my soft sheets." If you're not convinced by listening carefully to the original recording, then look at the whole chorus (and the whole song), and consider how much more sense "run for" makes.



In the first line of the chorus, "Fly" is an old-fashioned term meaning "run away from," so the speaker is telling his lover to LEAVE her willow branches and come wrap her body around his soul. He then rephrases the same idea as "Lay down your reeds and RUN FOR my soft sheets." In other words, both lines say, "Stop weaving that basket, Robin-Marie, and come have sex with me," which is something you might expect a sailor to say to his lover on the eve of a long whaling voyage.



I know, I know, all the lyric sites have "drums on," but that's probably because they all copy each other. Instead, I urge you to respect the hard work of skilled lyricists by using your own ears and your own understanding of the story the song is telling. Thank you!