Aims. In this work, we carry out a comprehensive study using galaxy data from the Lockman Spectroscopic Redshift Survey using Osiris (Lockman-SpReSO) project, a far-infrared (FIR) selected sample of galaxies observed using optical spectroscopy. We analyse a sub-sample of star-forming galaxies (SFGs) with secure spectroscopic redshifts, mostly in the luminous infrared (IR) galaxy domain. From these galaxies, parameters such as the extinction, star formation rate (SFR), and metallicity have been derived. The present paper examines how these properties evolve in relation to each other and in comparison with low-redshift FIR and non-FIR-selected samples of galaxies. Methods. We applied distinct selection criteria to attain an SFG sample with minimal AGN contamination. Multiple approaches were used to estimate the intrinsic extinction, SFR, and gas-phase metallicity for the SFGs. In conjunction with findings in the literature, we examined the correlation between SFRs and stellar masses (M_*), as well as the metallicity evolution depending on M_*. Finally, we also studied the 3D relationship between M_*, SFR, and metallicity. Results. From the initial spectroscopic sample of 409 FIR-selected objects from the Lockman-SpReSO catalogue, 69 active galactic nuclei (AGNs) were identified and excluded (17%), which is nearly double the percentage found in local studies, leaving us with a sample of 340 SFGs. The analysis of the M_*–SFR relationship revealed that Lockman-SpReSO IR-selected SFGs show signs of evolution at redshifts z > 0.4, shifting above the main sequence (MS), with a mean value of ∼0.4 dex. They are located within the starburst galaxy region since 78% of the galaxies fall into this category. In addition, no evident flattening was found in the relation to specific SFR with redshift for log M_* (M_⊙)≳10.5. In line with the M_*–metallicity relation (MZR) outcomes published in previous studies for optically selected SFGs; however, during the analysis of the MZR, it was found that IR-selected SFGs exhibit lower metallicities than the values anticipated on the basis of their M_* and redshift. During the investigation of the 3D M_*–SFR–metallicity relation (FP), it was established that the research sample is consistent with relations published in the existing literature, with an average scatter of ∼0.2 dex. However, a re-calibration of the FP when using the SFR obtained from the IR luminosity is required and, in this case, no attenuation in the correlation for log M_* (M_⊙)≳10.5 was observed. This result points to a possible evolution of the more massive fraction of the sample in the sense that the present-day star formation rate is lower with respect to the average rate of star formation in the past.