Getting access to the effective diffusion coefficient is a key point to provide realistic predictions of migration of radionuclides from radioactive waste repository in deep argillaceous geological formations. In the present work, the effective diffusion coefficient was computed inside an argillite micro-fracture as a function of its saturation level. The micrometric fracture geometry was extracted from the X-ray -tomography image ( voxel resolution) of an Opalinus clay sample. It was collected in the host rock excavated damaged zone surrounding a borehole in the Mont Terri laboratory. The computations were performed using two two-relaxation-time lattice Boltzmann models. The first one, a phase separation model, was used to extract the connected liquid phase inside the fracture for given saturations. The second, a diffusion model, was used to compute non-reactive tracer diffusion in the connected liquid phase of the fracture and to calculate the effective diffusion coefficient for the associated saturations. The dependence of the effective diffusion coefficient on saturation was found to be quasi-linear and to qualitatively match the Maxwell expression for saturations lower than 0.8.