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 an 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 AGE scars 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 AGE stars are at the very tip of the AGE and will not evolve significantly in luminosity before mass loss ends their AGE evolution. Derived mass-loss rates span a range from (M) over dot similar to 10(-7) to 10(-3) M. yr(-1). 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, Lie, 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, (M) over dot (nuc), for most of the RSGs. Two RSGs have (M) over dot much greater than (M) over dot (nuc), however, suggesting that RSGs shed most of their stellar mantles in short phases of intense mass loss. Stars on the thermal pulsing AGE may also experience episodes of intensified mass loss, but their quiescent mass-loss rates are usually already higher than (M) over dot (nuc).