  We present comprehensive observational results of the metallicity effect on
the fraction of globular clusters (GC) that contain low-mass X-ray binaries
(LMXB), by utilizing all available data obtained with Chandra for LMXBs and HST
ACS for GCs. Our primary sample consists of old elliptical galaxies selected
from the ACS Virgo and Fornax surveys. To improve statistics at both the lowest
and highest X-ray luminosity, we also use previously reported results from
other galaxies. It is well known that the LMXB fraction is considerably higher
in red, metal-rich, than in blue, metal-poor GCs. In this paper, we test
whether this metallicity effect is X-ray luminosity-dependent, and find that
the effect holds uniformly in a wide luminosity range. This result is
statistically significant (at >= 3 sigma) in LMXBs with luminosities in the
range LX = 2 x 10^37 - 5 x 10^38 erg s-1, where the ratio of LMXB fractions in
metal-rich to metal-poor GCs is R = 3.4 +- 0.5. A similar ratio is also found
at lower (down to 10^36 erg s-1) and higher luminosities (up to the ULX
regime), but with less significance (~2 sigma confidence). Because different
types of LMXBs dominate in different luminosities, our finding requires a new
explanation for the metallicity effect in dynamically formed LMXBs. We confirm
that the metallicity effect is not affected by other factors such as stellar
age, GC mass, stellar encounter rate, and galacto-centric distance.
