It is known that graphene reacts with atomic hydrogen to form a hydrogenated sheet of graphene. In order to understand the nature of the interaction between hydrogen and lithium in hydrogenated samples, we have carried out first principle calculations. Density functional theory and molecular dynamics were used to study the interaction between an icosahedron Li(13) cluster, and a graphene layer doped with a hydrogen atom. It was found that a hydrogen atom is levitated from the graphene layer and absorbed into the cluster of Li at 300 K and atmospheric pressure, with a binding energy far exceeding that of the adsorption energy of a hydrogen atom on the graphene layer.