  Utilising archival Chandra X-ray Observatory data and Hubble Space Telescope
globular cluster catalogues, we probe the time-domain properties of the low
mass X-ray binary population in the elliptical galaxy NGC 4261. Of the 98
unique X-ray sources identified in this study, 62 sources are within the
optical field of view and, of those, 33% are aligned with an optical cluster
counterpart. We find twenty X-ray sources coincident with globular clusters;
two are previously discovered ultra-luminous X-ray sources (ULXs) and eighteen
are low mass X-ray binaries (GCLMXBs) with $L_X < 10^{39}$ erg s$^{-1}$. ULXs
are a heterogeneous class of extremely bright X-ray binaries ($L_X > 10^{39}$
erg s$^{-1}$) and ULXs located in globular clusters (GCULXs) and may be
indicators of black holes. Identifying these unusually X-ray bright sources and
measuring their optical properties can provide valuable constraints on the
progenitors of gravitational wave sources. We compare observations of these
sources to the twenty previously-studied GCULXs from five other early-type
galaxies, and find that GCULXs in NGC 4261 are of similar colour and luminosity
and do not significantly deviate from the rest of the sample in terms of
distance from the galaxy centre or X-ray luminosity. Both the GCULX and low
mass X-ray binary (GCLMXB) populations of NGC 4261 show long term variability;
the former may have implications for fast radio bursts originating in globular
clusters and the latter will likely introduce additional scatter into the low
mass end of GCLMXB X-ray luminosity functions.
