It might be useful to point out something about "green sleeves" (note no caps there).

Clothing styles and technology at the time at least generally did not permanently make the sleeves part of the garment. Rather, they were "separates", which tied on to the body for the garment. It was common for a lady to have a number of sleeve sets, which were combined "for the nonce" with this or that garment.

That being said, I can see "My Lady Greensleeves" as being one who was fond of wearing sleeves of green. No grass stains necessary, even though the concept may be titillating to a modern audience.

Dave Oesterreich