Experimental and theoretical investigations of lower hybrid (LH) turbulence in the W7-AS stellarator are presented. The turbulence is excited by an ion beam, which is generated by a weak neutral hydrogen beam injected transversely to the confining magnetic field. The instability is detected by collective Thomson scattering of powerful gyrotron radiation. From the measured density dependence of the frequency it was identified as an LH type of instability. The spectrum is characterized by a narrow bandwidth in spite of the inherently poor radial resolution of the backscattering geometry. The theoretical model of an LH instability driven by a transverse fast ion component under the double resonance condition (coincidence of the LH frequency with a high cyclotron harmonic of the fast ions) is developed. The instability growth rate is derived. The stabilizing effect of high bulk ion temperatures was observed experimentally, in accordance with theoretical modelling. An instability saturation mechanism similar to the well known stochastic ion heating is proposed.