In order to further our understanding of the phenomena of X-ray emission from early-type galaxies, we obtained an optically flux-limited sample of 34 elliptical and S0 galaxies, observed with high and low angular resolution detectors on ROSAT. Our previous analysis of this sample suggested that the most X-ray-luminous galaxies were in rich environments. Here we investigate environmental influences quantitatively and find a positive correlation between L-X/L-B and the local galaxy density. Since the local galaxy density is usually related to the density of hot intergalactic gas, we suggest that this correlation occurs because the X-ray luminosity is enhanced, either through accretion of the intergalactic gas or because the ambient medium stifles galactic winds. When the ambient medium is unimportant, partial or global galactic winds can occur, reducing L-X/L-B. These effects lead to the large observed dispersion in L-X at fixed L-B. We discuss details of the data processing not previously presented, and examine the dependence of L-X on the choice of outer source radius and background location. We also compare the temperature deduced for these galaxies from different analyses of ROSAT and ASCA data. The ASCA and ROSAT temperatures are found to be similar, provided that the same metallicities and Galactic absorption columns are used.