We present numerical modeling of near Lower Hybrid (LH) grill Scrape-Off-Layer (SOL) plasma density variations as a function of gas puff and LH power with the fluid code EDGE-2D. The code includes direct SOL ionization by the LH wave. It is assumed that the ionization by the LH wave is produced due to the local SOL electron heating by the wave. Locally generated fast particles can also participate in the heating process. The EDGE2D code is now further updated to include effects due to near LH grill limiters, to model the so called private region of the grill. As is well known, the LH wave coupling critically depends on the plasma density in the private region just in front of the LH grill mouth. Trends in the modeled near LH grill plasma density variations are compared with trends in modeled ionization source profiles. In typical modeled cases relevant to experiments, these trends show an increase of near LH grill plasma density with increasing LH SOL heating and with increasing gas puff. The presence of the limiters in the modeling results in a different response of the private region density variation, and of the density variation in the Reciprocating Probe (RCP) location (where the density is measured), to the gas puff rate and to the SOL dissipated LH power. The density profile is higher and more flat in the RCP location, when the LH power dissipates more near to the separatrix. The results of the modeling are briefly compared with measurements of the SOL density, and with LH coupling trends observed in recent LH coupling experiments in JET.