  We derive the observable gravitational wave (GW) peak frequency ($f$)
distribution of binary black holes (BBHs) that currently reside inside their
globular clusters (GCs), with and without 2.5 Post-Newtonian (2.5PN) effects
included in the dynamical evolution of the BBHs. Recent Newtonian studies have
reported that a notable number of nearby non-merging BBHs, i.e. those BBHs that
are expected to undergo further dynamical interactions before merger, in GCs
are likely to be observable by LISA. However, our 2.5PN calculations show that
the distribution of $\log f$ for the non-merging BBH population above $\sim
10^{-3.5}$ Hz scales as $f^{-34/9}$ instead of the $f^{-2/3}$ scaling found in
the Newtonian case. This leads to an approximately two-orders-of-magnitude
reduction in the expected number of GW sources at $\sim 10^{-3}$ Hz, which lead
us to conclude that observing nearby BBHs with LISA is not as likely as has
been claimed in the recent literature. In fact, our results suggest that it
might be more likely that LISA detects the population of BBHs that will merge
before undergoing further interactions. This interestingly suggests that the
BBH merger rate derived from LIGO can be used to forecast the number of nearby
LISA sources, as well as providing insight into the fraction of BBH mergers
forming in GCs.
