The near-Earth space weather is driven by the quick release of magnetic free energy in the solar corona. Probing this extremely hot and rarified region of the extended solar atmosphere requires modeling the polarization of forbidden and permitted coronal lines. To this end, it is important to develop efficient codes to calculate the Stokes profiles that emerge from given three-dimensional (3D) coronal models and this should be done taking into account the symmetry breaking produced by the presence of magnetic fields and non-radial solar wind velocities. We have developed such a tool with the aim of theoretically predicting and interpreting spectropolarimetric observations of the solar corona in permitted and forbidden lines. In this paper, we show the results of a theoretical investigation of the linear polarization signals produced by scattering processes in the H I Lyα line at 1216 Å and in the He II Lyα line at 304 Å using 3D coronal models by Predictive Science Inc. These spectral lines have very different critical magnetic fields for the onset of the Hanle effect (53 G and 850 G, respectively), as well as different sensitivities to the Doppler effect caused by the solar wind velocities. We study under which circumstances simultaneous observations of the scattering polarization in these Lyα lines can facilitate the determination of magnetic fields and macroscopic velocities in the solar corona.