In this paper, we investigate via experimental and simulation techniques the transport properties, in terms of total ionic conductivity and ion diffusion coefficients, of ionic liquids doped with lithium salts. They are composed of two anions, bis(fluorosulfonyl)imide (FSI) and bis(trifluoromethanesulfonyl)imide (TFSI), and two cations, N-ethyl-N-methylimidazolium (emim) and lithium ions. The comparison of the experimental results with the simulations shows very good agreement over a wide temperature range and a broad range of compositions. The addition of TFSI gives rise to the formation of lithium dimers (Li+-TFSF--Li+). A closer analysis of such dimers shows that involved lithium ions move nearly as fast as single lithium ions, although they have a different coordination and much slower TFSI exchange rates.