Not sure where you're located, but the US post office provides free LP-shaped boxes when you ship via Priority mail. I've also constructed my own LP mailiers in the past by cutting and folding larger cardboard boxes down to LP size.
If it's an open lp, remove the vinyl and sleeve from the jacket. Place both jacket and lp with paper sleeve in a plastic outer jacket/sleeve. This protects the lp jacket from damage during shipping(the vinyl will tear the seams as it shifts around)