  The ROSAT-ESO Flux Limited X-ray (REFLEX) galaxy cluster survey and the 2dF
Galaxy Redshift Survey (2dFGRS) respectively comprise the largest, homogeneous
X-ray selected cluster catalogue and completed galaxy redshift survey. In this
work we combine these two outstanding datasets in order to study the effect of
the large-scale cluster environment, as traced by X-ray luminosity, on the
properties of the cluster member galaxies. We measure the LX-sigma relation
from the correlated dataset and find it to be consistent with recent results
found in the literature. Using a sample of 19 clusters with LX>=0.36*10^44 erg
s^-1 in the (0.1-2.4 keV) band, and 49 clusters with lower X-ray luminosity, we
find that the fraction of early spectral type (eta<=-1.4), passively-evolving
galaxies is significantly higher in the high-LX sample within R200. We extend
the investigation to include composite bJ cluster luminosity functions, and
find that the characteristic magnitude of the Schechter-function fit to the
early-type luminosity function is fainter for the high-LX sample compared to
the low-LX sample (Delta M*=0.58+/-0.14). This seems to be driven by a deficit
of such galaxies with M_bJ ~ -21. In contrast, we find no significant
differences between the luminosity functions of star-forming, late-type
galaxies. We believe these results are consistent with a scenario in which the
high-LX clusters are more dynamically evolved systems than the low-LX clusters.
