Molecular dynamics (MD) simulations have been carried out to study isotope effects in lithium hydride and lithium deuteride crystals. Quantum effects on nuclear motion have been included through a quantum thermal bath (QTB). The interatomic forces were described either within the density-functional theory (DFT) in the generalized gradient approximation (GGA) or by the phenomenological approach using the shell model. For both models, the isotopic shift in the lattice parameter can be successfully predicted by QTB-MD simulations. The slope of the experimental isotopic shift in pressure is satisfactorily reproduced by QTB-MD within DFT-GGA, in contrast to both density-functional perturbation theory and QTB-MD with the shell model. We have analyzed the reasons of these discrepancies through the vibrational densities of states and the isotopic shifts in bulk modulus. The results illustrate the importance of anharmonic contributions to vibrations and to the isotopic pressure shift between LiH and LiD.