For super soft lips in the morning, try applying lip balm/moisturiser to your lips before going to bed.
My absolute favorite lip balm is Rosebud Salve. What more can I say, 'it's the BEST'!!
You can also try the other balms from the Rosebud Perfume Co. in Mocha Rose, Menthol & Eucalyptus , Brambleberry Rose, Strawberry, and Minted Rose.