  In an earlier paper we presented nuclear X-ray flux densities, measured with
ROSAT, for the B2 bright sample of nearby low-luminosity radio galaxies. In
this paper we construct a nuclear X-ray luminosity function for the B2 radio
galaxies, and discuss the consequences of our results for models in which such
radio galaxies are the parent population of BL Lac objects. Based on our
observations of the B2 sample, we use Monte Carlo techniques to simulate
samples of beamed radio galaxies, and use the selection criteria of existing
samples of BL Lac objects to compare our simulated results to what is observed.
We find that previous analytical results are not applicable since the BL Lac
samples are selected on beamed flux density. A simple model in which BL Lacs
are the moderately beamed (gamma ~ 3) counterparts of radio galaxies, with some
random dispersion (~ 0.4 decades) in the intrinsic radio-X-ray relationship,
can reproduce many of the features of the radio-selected and X-ray-selected BL
Lac samples, including their radio and X-ray luminosity functions and the
distributions of their radio-to-X-ray spectral indices. In contrast, models in
which the X-ray and radio emission have systematically different beaming
parameters cannot reproduce important features of the radio-galaxy and BL Lac
populations. The redshift distribution and number counts of the X-ray-selected
EMSS sample are well reproduced by our best models, supporting a picture in
which these objects are beamed FRI radio galaxies with intrinsic luminosities
similar to those of the B2 sample. However, we cannot match the redshift
distribution of the radio-selected 1-Jy sample, and it is likely that a
population of FRII radio galaxies is responsible for the high-redshift objects
in this sample. [abridged]
