When I am helping mothers postpartum I usually help them learn how to breastfeed lying down. Learning to lie down and nurse is essential to getting night time sleep re-established for new moms.
The key is to practice nursing lying down during daytime feedings. Get comfortable and latch the baby on while lying down. Some women use the lower breast and others use the upper breast while the baby is raised on a cushion.
Practice for several days during nap time until you feel comfortable enough to try it at night. Think of nursing lying down as a skill that you will learn after you practice a while. It takes some coordination. Your patience will pay off. You will be able to nurse your baby at night while only partially waking up. This will help you get more rest. Remember to take daytime naps as a new mom. Sleep when your baby sleeps as much as you can.