The fourtheenth paper of the LIFE series (Cesario et al. 2024) has recently been accepted in Astronomy and Astrophysics. In this paper, we explore the potential of the Large Interferometer for Exoplanets (LIFE) for finding terrestrial protoplanets in their magma ocean phase that can yield insights into the prebiotic atmospheric conditions of rocky exoplanets. We assessed how various architecture and instrument designs for LIFE would alter the chances of detecting such a planet that is still hot and molten from its formation phase, and the distances for G- and M-dwarf exoplanet systems for which this would be possible. Our findings suggest that LIFE would be able to find and characterise terrestrial protoplanets in young planet-forming systems up to a distance of about 100 pc from the Solar System, which includes a number of prominent star-forming regions suitable for these observations. The study highlights the importance of the short wavelength interval less than 6 microns for characterising such planets, and motivates an extension of the target systems beyond the nominally considered distance range for LIFE. Follow-up studies are planned to look into how well LIFE can retrieve the atmospheric composition of such protoplanets and the expected distribution of protoplanets in the most suitable young planetary systems.