I slept on my back for about 4 weeks after LD surgery, as tried my best to keep off the newly reconstructed breast.
I slept with a v pillow to prop me up to make it more comfortable and put a pillow in the hollow of my back as that started to ache as I normally sleep on my back. I did have to sometimes take painkillers for the pain in my back which I never normally suffer from.
It was well worth a few weeks discomfort though.
Good Luck wih your surgery.