Context. Classical novae are known to demonstrate a supersoft X-ray source (SSS) state following outbursts. This state is associated with residual thermonuclear burning on the white dwarf (WD) surface. During its all-sky survey (eRASS1), the eROSITA telescope on board the Spectrum-Roentgen-Gamma observatory discovered a bright new SSS, whose position is consistent with the known classical nova AT 2018bej in the Large Magellanic Cloud. There were two eROSITA spectra obtained during the eRASS1 and eRASS2 monitoring epochs and one XMM-Newton grating spectrum close to the eRASS1 epoch. Aims. We aim to describe the eROSITA and follow-up XMM-Newton spectra of AT 2018bej with our local thermodynamic equilibrium (LTE) atmosphere models. We focussed on the evolution of the hot WD properties between the eRASS1 and eRASS2 epochs, especially with respect to the change in carbon abundance. Methods. A grid of LTE model atmosphere spectra was calculated for different values of the effective temperature (from Teff = 525 to 700 kK in steps of 25 kK), surface gravity (six values), and chemical composition, assuming approximately equal hydrogen and helium number fractions, and five different values of carbon and nitrogen abundances. Results. Both eRASS1 and XMM 0.3–0.6 keV spectral analyses yield a temperature of the WD of Teff~ 600 kK and a WD radius of 8000–8700 km. A simultaneous fitting of the eROSITA spectra for two epochs (eRASS1 and eRASS2) with a common WD mass parameter demonstrates a decrease in Teff, accompanied by an increase in the WD radius and a decrease in the carbon abundance. However, these changes are marginal and remain within the errors. The derived WD mass is estimated to be 1.05–1.15 M⊙. Conclusions. We traced a minor evolution of the source on a half-year timescale accompanied by a decrease in the carbon abundance and concluded that LTE model atmospheres can be used to analyse the available X-ray spectra of classical novae during their SSS state.