Non-local spin injection in lateral spin valves generates a pure spin current which is a diffusive flow of spins (i.e. spin angular momentums) with no net charge flow. The diffusive spins lose phase coherency in precession while undergoing frequent collisions and these events lead to a broad distribution of the dwell time in a transport channel between the injector and the detector. Here we show the lateral spin-valves with dual injectors enable us to detect a genuine in-plane precession signal from the Hanle effect, demonstrating the phase coherency in the in-plane precession is improved with an increase of the channel length. The coherency in the spin precession shows a universal behavior as a function of the normalized separation between the injector and the detector in material-independent fashion for metals and semiconductors including graphene.