The diffusion of a lithium salt through a diblock copolymer electrolyte was studied using vibrational spectroscopy. Lithium bis-trifluoromethylsulfonimide (LiTFSI) was dissolved in a lamellar-structured, high-molecular-weight polystyrene-poly(ethylene oxide) diblock copolymer at various concentrations (0-4.51 molLiTFSI/kg(PEO)). The diffusion coefficient of LiTFSI was determined from time-resolved Fourier Transform infrared spectroscopy attenuated total reflectance (FTIR-ATR) as a function of the salt concentration. By the application of the Beer-Lambert law, FTIR-TR was used to detect concentration changes. Mutual diffusion was driven by putting in contact two polymer electrolyte membranes with different salt concentrations. Thus, mutual diffusion coefficients were obtained without the influence of electric fields or electrode interfaces. The accuracy of the simple experimental approach and straightforward analysis was validated by comparison to diffusion coefficients reported from measurements in electrochemical cells. Both methods yield mutual diffusion coefficients of lithium salt that are only weakly (and nonmonotonically) dependent on salt concentration. There is some indication in the spectra that there exist two populations of salt with different dissociation states. This could explain the observed nonmonotonic concentration dependence of the mutual diffusion coefficient of the salt. This hypothesis will be examined quantitatively with complementary measurements in future work.