Left: L_X/SFR as a function of galaxy gas-phase metallicity for the eFEDS-HECATE galaxies classified as star-forming. L_X represents the integrated galaxy X-ray luminosity (XRBs + hot gas). We overlay Lyman break analogues from (Basu-Zych et al. 2013b, unfilled black circles) and Jia et al. (2011, filled grey plusses), local star-forming galaxies from Colbert et al. (2004, filled grey squares) and Mineo et al. (2012a, filled grey diamonds), and luminous or ultraluminous infrared galaxies from Lehmer et al. (2010, inverted filled grey triangles) and Iwasawa et al. (2011, filled grey triangles). The blue hatched region shows the range of values for z = 2 Lyman break galaxies (Basu-Zych et al. 2013b). The theoretical prediction from Fragos et al. (2013) for HMXBs is shown as a solid dark grey line. The dashed blue line represents the average integrated (hot gas + HMXBs) L_{0.5–2 keV}/SFR of normal galaxies from Lehmer et al. (2016). We do not have metallicity estimates for eFEDS-HECATE galaxies classified using 6dF spectra (Sect. 2.3). The dot-dashed black line with grey dispersion shows the best-fit to the eFEDS-HECATE star-forming galaxies. The sample shows elevated L_X/SFR across metallicity, especially at low metallicity. This may be due to an obscured AGN, excessive contribution from hot gas, or increased HMXB emission (see Sect. 4.2). Right: L_X-SFR-metallicity relation from Brorby et al. (2016) showing the best-fit from their paper for integrated L_{0.5–8 keV} Lyman break analogues (dashed grey line with dispersion in dark grey). The offset between the eFEDS-HECATE galaxies and the relation for Lyman break analogues is pronounced towards low-SFR and low-metallicity.