Continuous-wave linewidths and spin susceptibilities, spin-spin relaxation rates (1/T-2), and spin-lattice relaxation rates (1/T-1) for two sources of x-LiPc were measured at 9.5 GHz between 15 and 298 K. Relaxation rates at 34 GHz were measured between 80 and 298 K. Room-temperature relaxation rates also were measured at 250 MHz, 1.9 GHz, and 2.76 GHz. The temperature dependences of linewidths and spin susceptibilities are characteristic of 1-D organic conductors. The ratio of populations of localized and delocalized electrons varies with sample preparation. For a single needle between 15 and about 200 K, 1/T-2 is higher for the parallel orientation, but 1/T-1 is higher for the perpendicular orientation, consistent with predictions based on dipolar interactions. Between about 60 and 150 K, which is the temperature regime in which spin susceptibility is changing rapidly with temperature, 1/T-1 exhibits a non-monotonic dependence on temperature and is lower at 34 GHz than at 9.5 GHz. In other organic conductors, this dependence has been attributed to a bottleneck mechanism of relaxation. At higher temperatures, 1/T-1 becomes less orientation-dependent. At room temperature, T-1 increases rapidly between 250 MHz (3.0 mu s) and 2.76 GHz (6.3 mu s) and then shows less frequency dependence up to 34 GHz (9.8 mu s). The relaxation rate near room temperature might have a substantial contribution from spin hopping perpendicular to the stacking axis of the molecules.