It is known that Lower Hybrid (LH) wave increases the Scrape-off-Layer (SOL) density by direct ionization of the SOL due to parasitic LH wave energy absorption. Similarly, also ELMs bring energy into the SOL, the SOL temperature is increased and the SOL ionization is enhanced. In this paper we present a modeling study of modifications in time of the JET SOL due to ELM events and direct SOL LH ionization. The modeling uses the fluid code EDGE2D, upgraded to include direct SOL ionization by the LH wave and the effect of the limiters near the LH grill simulating the LH grill private space. It follows from the modeling that the SOL density nSOL is higher during LH due to the direct LH SOL ionization, but the additional nSOL variations corresponding to ELMs are lower in front of the LH grill, where the LH power is dissipated. As the computations show, most of the SOL neutrals are ionized by the LH parasitic dissipation before the ELM arrives, so that any additional contribution to the ionization of the SOL due to ELMs can only be small. This explains the reduction in variations of the LH wave reflection coefficient observed experimentally in ELMy plasmas when the LH power is increased. The modeled nSOL variations due to ELMs and LH ionization, and variations in the ion saturation currents density jsat are in a good agreement with nSOL and jsat measured by the ReciProcating Probe (RCP). For comparison with experiments, the modeled Dalpha line intensity is integrated along the standard diagnostic vertical line of sight from the top of the machine to the outer divertor apron. However, here the modeling does not exhibit the observed strong enhancement of the Dalpha peaks during ELMs, when the LH power is on. This discrepancy is due to the fact that the fluid code EDGE2D can not in its present form account for all effects of the fast particles generated in front of the LH grill.