We have determined the location of the line-opacity modified
Eddington limit for stars in the LMC using the most recent atmosphere
models combined with a precise mapping to the HR Diagram through
up-to-date stellar evolution calculations. While we find, in
agreement with previous studies, that the shape of the modified
Eddington limit qualitatively corresponds to the
Humphreys-Davidson (HD) limit defined by the most luminous
supergiants, the modified limit is actually a full magnitude
higher than the upper luminosity limit observed for LMC stars. The
observed limit is consistent with atmosphere models in which the
maximum value of the ratio of the radiation force outwards to the
gravitational force inwards, Y_max, is 0.9, i.e., the
photospheres of stars at the observed luminosity limit are bound. As
massive stars evolve, they move to higher, and therefore less stable
values of Y_max, so mass loss, either sporadic or continuous,
may halt their natural redward evolution as they approach the Y_max = 0.9 limit.
We assess the metallicity dependence of this
limit. If the limit does determine the most luminous stars, and the
value of Y_max corresponding to the luminosity limit in the
LMC is universal, then the brightest supergiants the SMC should be
only marginally brighter (0.3mag) than those of the LMC, in agreement
with observations. Moreover, the brightest supergiants in M31 should
be 0.75mag fainter than those in the LMC.