We investigate the relationship between soft X-ray luminosity and mass for low-redshift clusters of galaxies by comparing observed number counts and scaling laws to halo-based expectations of ΛCDM cosmologies. We model the conditional likelihood of halo luminosity as a lognormal distribution of fixed width, centered on a scaling relation, L M^pρ(z), and consider two values for s, appropriate for self-similar evolution or no evolution. Convolving with the halo mass function, we compute expected counts in redshift and flux that, after appropriate survey effects are included, we compare to REFLEX survey data. Counts alone provide only an upper limit on the scatter in mass at fixed luminosity, σ_{ln M} < 0.4. We argue that the observed, intrinsic variance in the temperature-luminosity relation is directly indicative of mass-luminosity variance and derive σ_{ln M} = 0.43 ± 0.06 from HIFLUGCS data. When added to the likelihood analysis, we derive values p = 1.59 ± 0.05, ln L_15,0 = 1.34 ± 0.09, and σ_{ln M} = 0.37 ± 0.05 for self-similar redshift evolution in a concordance (Ω_m = 0.3, Ω_Λ = 0.7, σ₈ = 0.9) universe. The present-epoch intercept is sensitive to power spectrum normalization, L_15,0 σ, and the slope is weakly sensitive to the matter density, p Ω. We find a substantially (factor 2) dimmer intercept and slightly steeper slope than the values published using hydrostatic mass estimates of the HIFLUGCS sample and show that a Malmquist bias of the X-ray flux-limited sample accounts for this effect. In light of new WMAP constraints, we discuss the interplay between parameters and sources of systematic error and offer a compromise model with Ω_m = 0.24, σ₈ = 0.85, and somewhat lower scatter σ_{ln M} = 0.25, in which hydrostatic mass estimates remain accurate to ~15%. We stress the need for independent calibration of the L-M relation via weak gravitational lensing.