Materials which possess a high lithium ion conductivity are very attractive for battery and fuel cell applications. Hydrogenation of the fast-ion conductor lithium nitride (Li3N) leads to the formation of lithium imide (Li2NH) and subsequently of lithium amide (LiNH2). Using ab initio molecular dynamics simulations, we carried out a comparative study of the Li diffusion in these three systems. The results demonstrate that hydrogen can work as both promoter and inhibitor of Li mobility, with the lowest transition temperature to the superionic state occurring in Li2NH. Furthermore, we show that the creation of Li vacancies strongly affects Li diffusion in Li3N, but not so in Li2NH. Finally, we explain our findings with the help of a simple model.