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 ratioof the heat capacity amplitudes, above and below the NL_α transition, and the corresponding critical exponent α on seven C_sPFO concentraions remain near 1 and 0, respectively, suggesting that the transition is a second order in agreement with 3-d XY type behabior. The longitudinal correlation length ξ∥ and the susceptibility σassociated with the lamellar phase fluctuations in the N phase at a concentration 46.6 wt% CsPFO were measured over three decades of reduced temperature and found to diverge with critical exponent v∥0.86±0.04 and γ=1.37±0.11, respectively.