L.I. Lobkovsky's main research interests are related to the application of continuum mechanics methods to solving problems of geodynamics, marine Geology and Geophysics, and Oceanology. He developed quantitative geodynamic models of the processes of spreading and subduction of the ocean lithosphere, cycles of the strongest tsunamigenic earthquakes, collisions of lithospheric plates, evolution of passive continental margins, sinking of the basement of sedimentary basins; proposed the concept of two-tier plate tectonics; predicted the strongest tsunamigenic earthquakes in the Central Kuril Islands in 2006–2007. The processes of propagation of the corresponding tsunami waves in the Pacific Ocean and the sea of Okhotsk are modeled; a thermochemical model of mantle convection is proposed, which is used for numerical modeling of the global evolution of the Earth throughout its history.