We have investigated multiple scattering of light in a disordered system based on liquid crystals for a temperature-controllable random laser. Coherent backscattering measurements at several temperatures have been well fitted by the theoretical model deduced for a random collection of spherical point scatters based on a diffusion approximation. The transport mean free path exclusively depends on the diffusivity of the liquid crystalline phase of the hybrid scattering system. It is shown how the laser threshold excitation intensity is strongly correlated with the transport mean free path.