The study of lunar plasma environment’s response to the magnetotail lobe condition is the main subject of our investigation in this report. Photoionization and charge exchange of protons with the lunar exosphere arethe ionization processes included in our model. The computational model includes the dynamics of heavy Na+ pickup and ambient magnetospheric ions. The electrons are considered as a fluid.The lunar interior is considered as a weakly conducting body. In this report we consider for the first time a formation of lunar plasma structures, wakes, and a generation of low-frequency electromagnetic waves by using a self-consistent hybrid kinetic modeling. The input parameters were taken from the ARTEMIS observations. At an early stage the Moon with exosphere and conducting core excites whistler waves in case of Sub-Alfvenic/sonic interaction. At a later stage an excitation of the Alfven wave is observed. The topology of the Alfven waves is approximately similar to the Alfven wing near the planetary moons (Io, Europa etc.). The physics of the Moon-magnetotail lobe interaction is also close to the physics of the interaction between plasma clouds (expanding and not expanding) and ambient magnetospheric plasma. The heavy pickup ions create a large structured halo with space scale of more than 10 R_{E} in the direction of the background field. The modeling also shows an excitation of the compressional waves due to expansion of heavy exospheric pickup ions. The lunar model with weaker interior conductivity excites lower levels of the wave activity. This work was supported by NASA Award (80NSSC20K0146) from Solar System Workings Program (NNH18ZDA001N-C.3-SSW2018). Computational resources were provided by the NASA High-End SupercomputingFacilities (Aitken-Ames, Project HEC SMD-20-02357875).