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.
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