  In this work we conclude the analysis of our CO line survey of Luminous
Infrared Galaxies (LIRGs: L_{IR}>=10^{11}L_{sol}) in the local Universe
(Paper\,I), by focusing on the influence of their average ISM properties on the
total molecular gas mass estimates via the so-called X_{co}=M(H_2)/L_{co,1-0}
factor. One-phase radiative transfer models of the global CO Spectral Line
Energy Distributions (SLEDs) yield an X_{co} distribution with:
<X_{co}>\sim(0.6+/-0.2) M_{sol}(K km s^{-1} pc^2)^{-1} over a significant range
of average gas densities, temperatures and dynamical states. The latter emerges
as the most important parameter in determining X_{co}, with unbound states
yielding low values and self-gravitating states the highest ones. Nevertheless
in many (U)LIRGs where available higher-J CO lines (J=3--2, 4--3, and/or
J=6--5) or HCN line data from the literature allow a separate assessment of the
gas mass at high densities (>=10^{4} cm^{-3}) rather than a simple one-phase
analysis we find that {\it near-Galactic X_{co} (3-6)\,
M_sol\,(K\,km^{-1}\,pc^2)^{-1} values become possible.} We further show that in
the highly turbulent molecular gas in ULIRGs a high-density component will be
common and can be massive enough for its high X_{co} to dominate the average
value for the entire galaxy. .........
  ...this may have thus resulted to systematic underestimates of molecular gas
mass in ULIRGs.
