Hydrogen is relatively simple to produce from renewable electricity, a clean energy carrier and a carbon-free alternative fuel. Therefore, the interest in developing models that can predict hydrogen combustion is continuously increasing. However, the high diffusivity of hydrogen poses a challenge, since it leads to strong wrinkling of the flame and fluctuations of elements mass fractions and enthalpy along the flame front, which are difficult to model. In this study, we investigate how the Flamelet-Generated Manifold (FGM) technique can be applied to model these phenomena. We performed Direct Numerical Simulations (DNS) of two cases with detailed chemistry and different Reynolds numbers, as a benchmark to study how well several manifolds can predict the behaviour of these flames. Then, we built several manifolds varying different parameters, such as equivalence ratio, temperature, stretch and heat release rate, both dependently and independently, in order to account for the fluctuations along the flame front caused by preferential diffusion. We found that two dimensional manifolds with equivalence ratio fluctuations are sufficient to predict the main species mass fractions, however, three-dimensional manifolds with independent variation of equivalence ratio and enthalpy, resulted in a more accurate prediction of radicals mass fractions, source terms, and turbulent burning velocity. For increasing Reynolds numbers, the discrepancies between the FGM and the DNS increase slightly. These results represent an advance in the development of a model for lean turbulent hydrogen combustion, further facilitating the execution of simulations of these types of flames in complex geometries such as gas turbines.