The sensitivity of lossy mode resonance (LMR)-based sensors to the change in the surrounding medium refractive index (SMRI), which has optical constants of water, was determined. The calculations were performed for a cylindrical light guide with a diameter of 18 μm and a length of 4 mm, having the parameters of a standard single-mode optical fiber SMF-28 with a partially removed cladding, coated with a thin film of material with a refractive index in the range from 1.7 to 3.4. It was found that if the refractive index of the thin film approximately equals two, the SMRI-sensitivities of the first transverse electric (TE) and transverse magnetic (TM) LMRs coincide, and the maximum sensitivity of all TM resonances occurs. According to the computations, when the absolute value of the coating material chromatic dispersion increases, the first LMRs sensitivities decrease. This effect is more significant for the TE resonance. It was demonstrated that in the case of using a coating with a refractive index less than 1.93 the SMRI-sensitivity of the first TM LMR is higher than that of the first TE LMR for any quantity the material chromatic dispersion.