The nematic (N) to lamellar (L_α) phase transition in binary mixtures of cesium perfluorooctanoate (C_SPFO) and water has been studied by high-precision calorimetry and high-resolution synchrotron x-ray scattering. The artio of the heat capacity amplitudes, above and below the NL_α transition, and the corresponding critical exponent α on seven C_SPFO concentrations remain near 1 and 0, respectively, suggesting that the transition is a second order in agreement with 3-d XY type behavior. The longitudinal correlation length_II and the susceptibility associated with the lamellar phase fluctuations in the N phase at the concentration 46.6 wt% C_SPFO were measured over three decades of reduced temperature and found to diverge with critical exponent , respectively.