Lower Hybrid (LH) Current Drive experiments have been carried out on JET with a gap varying between 0.09 and 0.16m, and LH power in the range of 0-3.2MW. For different plasma configurations, the electron density ne of the scrape-off layer has been studied by the mean of a reciprocating Langmuir probe magnetically connected to the LH antenna. For pulses in the high confinement regime (H mode) characterized by strong particle bursts in the plasma edge, the Edge Localized Modes (ELMs), profiles of the saturation current (Jsat) are obtained with a sufficient time resolution to distinguish 'between ELMs' and during the rise and decay of the ELMs. It is found that gas injection from a valve located near the LH launcher and magnetically connected to it allows to rise the density and improve the LH coupling. The Jsat profiles indicate quite clearly that this density rise affects mainly the plasma layer in front of the antenna with a typical thickness of 5cm. The resulting profile can be extremely flat in this region. The effect of the near-launcher gas injection but also of the LH power and the total gas injection on the density at the wall is quantitatively documented. It is shown in particular that with increasing LH power, the required gas injection for obtaining good LH coupling is decreasing, with no saturation obtained so far. Effect of the ELMs on the LH coupling is also discussed. Modelling with the EDGE2D code indicates that such flat profiles of Jsat/ne can be obtained when LH power dissipation is taken into account. Detailed analysis of the heat flux carried by electrons accelerated in the near-field of the antenna confirms the increase of density with gas puff during high LH power coupling.