We present in this paper modeling of the JET Scrape-Off-Layer (SOL) including direct SOL ionization by launched LH (Lower Hybrid) waves. For that purpose, the two dimensional fluid code EDGE2D-NIMBUS was modified in order to account for possible enhanced ionization in the SOL due to the LH power absorbed by the electrons in a layer extending in the radial direction from the launcher. By taking the direct LH SOL ionization into account, the observed modification of the density in front of the LH antenna during LH power and gas injection can be explained. The JET grill private SOL limiters acting as sinks for the particles are also included in the model. We compare the efficiency of gas puffing from the Top and the Outer Mid-Plane (OMP) for SOL density enhancement and improvement in LH coupling. The observed reduction of the temporal variation of the LH wave reflection coefficient and of measured saturated currents in the SOL during ELMs is explained. The density depletion by ponderomotive forces in front of the grill is estimated.