We present a detailed X-ray spectral analysis of the active galactic nucleus (AGN) population in the Lockman-SpReSO project, a multiwavelength campaign of FIR sources in the Lockman Hole field. Using deep XMM-Newton observations cross-matched with FIR-selected galaxies, we characterize 94 AGNs based on their X-ray spectral properties. The sample is distributed over a large redshift range of $z = 0.07{-}5$, and reaches a flux limit of $5 \times 10^{-16}\, \mathrm{erg\, s^{-1}\, cm^{-2}}$ in the $0.3{-}10\, \mathrm{keV}$ band. We model the X-ray spectra using absorbed power-law, reflection, and soft excess components to estimate intrinsic column densities ($N_{\mathrm{H}}$), rest-frame $2{-}10\, \mathrm{keV}$ luminosities, and iron line equivalent widths (EWs). Additionally, we included an advanced model fitting for Compton-thick AGNs (CT-AGNs) using the XCLUMPY model. Our results show an increase in the fraction of obscured AGNs towards higher redshifts, including the identification of one strong and two borderline CT-AGN candidates with $N_{\mathrm{H}} \gtrsim 10^{24}\, \mathrm{cm^{-2}}$. Soft excess emission is detected in 10 AGNs, with an average blackbody temperature of $0.12 \pm 0.02\, \mathrm{keV}$. We also detect the X-ray Baldwin effect in both obscured and unobscured populations, and we found a strong correlation between the torus angular width $(\sigma _\mathrm{tor})$, dust covering factor $(f_{\mathrm{cov}})$, and X-ray luminosity, described by $f_{\mathrm{cov}} = (-0.1 \pm 0.01) \times \log (L_{2-10\, \mathrm{keV}}/(10^{44}\, \mathrm{erg\, s^{-1}})) + (0.65 \pm 0.01)$, supporting the receding torus scenario. While consistent with deep X-ray surveys, the FIR selection favours the identification of dusty star-forming host galaxies and heavily obscured AGNs.