Amphiphilic lipid bilayers modify the friction properties of the surfaces on top of which they are deposited. In particular, the measured sliding friction coefficient can be significantly reduced compared with the native surface. We investigate in this work the friction properties of a numerical coarse-grained model of DSPC (1,2-distearoyl-sn-glycero-3-phosphocholine) lipid bilayer subject to longitudinal shear. The interleaflet friction coefficient is obtained from out-of-equilibrium pulling or from relaxation simulations. In particular, we gain access to the transient viscoelastic response of a sheared bilayer. The bilayer mechanical response is found to depend significantly on the membrane physical state, with evidence in favor of a linear response regime in the fluid but not in the gel region. The linear response validity domain is established, and the timescales appearing in the membrane response discussed.