We study the kinetics of the lateral hole transfer occurring between dye molecules anchored at the surface of the metal oxide in Dye Sensitized Solar Cells (DSSC). We use Marcus' charge transfer rate equation for which we need the electronic coupling between two molecules (J) and the reorganization energy (λtot). In DSSC the medium surrounding the dyes is highly polar. This means that the contribution of the solvent to the reorganization energy cannot be neglected. Here we elaborate a method to calculate, from first principles, the total (i.e., inner- and outer-sphere) reorganization energy of hole exchange between ruthenium dyes. The influence of the solvent and of the ions in the solvent is incorporated. The inner-sphere reorganization energy depends on the nature of the dye, 0.1 eV for ruthenium dyes with CN ligands, 0.2 eV for ruthenium dyes with NCS ligands. In acetonitrile, the solvent reorganization energy contributes for at least 80% of the total giving a total reorganization energy of around 0.86 eV for ruthenium dyes with CN ligands and 0.95 eV for ruthenium dyes with NCS ligands. We use these results to estimate the rate of hole transfer within Marcus theory. We suggest that low diffusion coefficients observed experimentally may arise from the high polarity of the medium rather than by the chemical structure of the dye.