We investigate the relationship between soft xray luminosity and mass for low redshift clusters of galaxies by comparing observed number counts to expectations of $Lambda$CDM cosmologies. We use a three-parameter model for the conditional probability of luminosity given mass and epoch, described as a log-normal distribution of fixed width centered on a power-law scaling relation, $L spropto M^prhoc^s(z)$. We use an ensemble of simulated clusters to argue that the observed, intrinsic variance in the temperature--luminosity relation is directly indicative of mass--luminosity variance, and derive $sigm se 0.43 pm 0.06$ from HIFLUGCS data. Adding this to the likelihood analysis results in best-fit estimates $p se 1.59 pm 0.05$, $lnlf se 1.34 pm 0.09$, and $sigm se 0.37 pm 0.05$ for self-similar redshift evolution in a concordance ($Omega_m se 0.3$, $Omega_Lambda se 0.7$, $sigma_8 se0.9$) universe. We show that the present-epoch intercept is very sensitive to power spectrum normalization, $lnlf spropto sigate^{-4}$, and the slope is weakly sensitive to the matter density, $p spropto Omega_m^{1/2}$. The intercept derived here is dimmer by a factor 2, and slope slightly steeper, than the L-M relation published using hydrostatic mass estimates of the HIFLUGCS sample. We show that this discrepancy is largely due to Malmquist bias of the xray flux-limited sample. In light of new WMAP constraints, we discuss the interplay between parameters and sources of systematic error, and offer a compromise model with $Omega_m se 0.24$, $sigma_8 se 0.85$, and somewhat lower scatter $sigm se 0.25$, in which hydrostatic mass estimates remain accurate to $ssim 15%$. We stress the need for independent calibration of the L-M relation via weak gravitational lensing.
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