The "style," or process of having intercourse with a lamb or adult sheep. It may also describe the act of fornicating with other similar barnyard animals, as well.
Generally, this is a derogatory phrase used to indicate that an individual, typically male, is of a very rural, "backwoods" culture or environment. It is used to indicate that an individual either has sex with the aforementioned animals, or acts as though he is having sex with them during human to human intercourse.
Your sister's dating that dude? He's so hillbilly, he'll probably screw her sheepy style!