We present an improved model relating the frequency shift between 133Cs hyperfine Zeeman substates to the Lorentz-violating coefficients of the Standard-Model Extension (SME) framework. This model is based on a second order boost Lorentz transformation, which enables us to constrain the isotropic coefficient CTT. It also takes into account the nuclear structure, beyond the usual Schmidt model, extending the scope of the analysis from purely proton to both proton and neutron coefficients. Applying this advanced model to FO2 133Cs cold atom fountain clock data, previously analyzed in [P. Wolf et al., 2006], we improved by up to 13 orders of magnitude the present maximum sensitivities for laboratory tests, reaching the generally expected suppressions scale at which signatures of Lorentz violation could appear.