Oxygen mobility in layered lanthanum cuprates La2-xSrxCuO4-delta is studied by dynamic-thermal isotope exchange method and coulometric titration. Depending on the temperature, different preferred surface exchange reactions are realized. Such characteristics of bulk diffusion process as activation energy and diffusion coefficient are stated for the cuprates. Theoretical modeling of diffusion process in La2CuO4 and LaSrCuO3.5 phases is carried out using molecular dynamics simulations. The data obtained are compared to the ones previously obtained experimentally.