Abstract Gravitational lensing may render individual high-mass stars detectable out to cosmological distances, and several extremely magnified stars have in recent years been detected out to redshifts z ≈ 6. Here, we present Muspelheim, a model for the evolving spectral energy distributions of both metal-enriched and metal-free stars at high redshifts. Using this model, we argue that lensed stars will form a highly biased sample of the intrinsic distribution of stars across the Hertzsprung-Russell diagram, and that this bias will typically tend to favour the detection of lensed stars in evolved stages characterized by low effective temperatures, even though stars only spend a minor fraction of their lifetimes in such states. We also explore the prospects of detecting individual, lensed metal-free (Population III) stars at high redshifts using the James Webb Space Telescope (JWST). We find that very massive (≳ 100 M⊙) Population III stars at z ≳ 6 may potentially be detected by JWST in surveys covering large numbers of strong lensing clusters, provided that the Population III stellar initial mass function is sufficiently top-heavy, that these stars evolve to effective temperatures ≤15000 K, and that the cosmic star formation rate density of Pop III stars reaches ≳ 10−4 M⊙ cMpc−3 yr−1 at z ≈ 6–10. Various ways to distinguish metal-free lensed stars from metal-enriched ones are also discussed.