A radiative transfer code is used to model the spectral energy distributions of 57 mass-losing Asymptotic Giant Branch (AGB) stars and red supergiants (RSGs) in the Large Magellanic Cloud (LMC) for which ISO spectroscopic and photometric data are available. As a result we derive mass-loss rates and bolometric luminosities. A gap in the luminosity distribution around M_bol = -7.5 mag separates AGB stars from RSGs. The luminosity distributions of optically bright carbon stars, dust-enshrouded carbon stars and dust-enshrouded M-type stars have only little overlap, suggesting that the dust-enshrouded AGB stars are at the very tip of the AGB and will not evolve significantly in luminosity before mass loss ends their AGB evolution. Derived mass-loss rates span a range from Mdot about 10^-7 to 10^-3 M_sun/yr. More luminous and cooler stars are found to reach higher mass-loss rates. The highest mass-loss rates exceed the classical limit set by the momentum of the stellar radiation field, L/c, by a factor of a few due to multiple scattering of photons in the circumstellar dust envelope. Mass-loss rates are lower than the mass consumption rate by nuclear burning, Mdot_nuc, for most of the RSGs. Two RSGs have Mdot >> Mdot_nuc, however, suggesting that RSGs shed most of their stellar mantles in short phases of intense mass loss. Stars on the thermal pulsing AGB may also experience episodes of intensified mass loss, but their quiescent mass-loss rates are usually already higher than Mdot_nuc.
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