LiF doped LIFO, glasses have been investigated by means of nuclear magnetic resonance. Spin-lattice relaxation rates of the stationary P-31 nucleus have been measured in both the laboratory and the rotating frame of reference, thus covering the wide frequency range from about 34 kHz to 81 MHz. The temperature acid frequency dependence of the rates is described by the Bloembergen-Purcell-Pound model, modified with a Gaussian distribution of activation energies. For doped and undoped samples, the derived values for the activation energy of the lithium motion compare well with those obtained by DC conductivity measurements. We also report on aging effects in the glassy samples.