We calculate the contribution to the polarization of Lambda hyperons in relativistic nuclear collisions at high energy from the decays of Sigma ^{*}(1385) and Sigma ^0, which are the predominant sources of Lambda production besides the primary component, as a function of the Lambda momentum. Particularly, we estimate the longitudinal component of the mean spin vector as a function of the azimuthal angle in the transverse plane, assuming that primary Sigma ^{*} and Sigma ^0 polarization follow the predictions of local thermodynamic equilibrium in a relativistic fluid. Provided that the rapidity dependence around midrapidity of polarization is negligible, we find that this component of the overall spin vector has a very similar pattern to the primary one. Therefore, we conclude that the secondary decays cannot account for the discrepancy in sign between experimental data and hydrodynamic model predictions of the longitudinal polarization of Lambda hyperons recently measured by the STAR experiment at RHIC.