Lipid membranes in a physiological context cannot be understood without taking into account their mobile environment. Here, we report on a high energy-resolution neutron backscattering study to investigate slow motions on nanosecond time scales in highly oriented solid supported phospholipid bilayers of the model system DMPC -d54 (deuterated 1,2-dimyristoyl-sn-glycero-3-phoshatidylcholine). This technique allows discriminating the Q-dependent onset of mobility and provides a benchmark test regarding the feasibility of dynamical neutron scattering investigations on these sample systems. Apart from freezing of the lipid acyl-chains, we could observe a second freezing temperature that we attribute to the hydration water in between the membrane stacks. The freezing is lowered several degrees as compared to (heavy) bulk water.