  I study the potential role of young massive (YMCs) and open star clusters
(OCs) in assembling stellar-mass binary black holes (BBHs) which would be
detectable as persistent gravitational-wave (GW) sources by the forthcoming
LISA mission. The energetic dynamical interactions inside star clusters make
them factories of assembling BBHs and other types of double-compact binaries
that undergo general-relativistic (GR) inspiral and merger. The initial phase
of such inspirals would, typically, sweep through the LISA GW band. Here, such
LISA sources are studied from a set of evolutionary models of star clusters
with masses ranging over $10^4M_\odot-10^5M_\odot$ that represent YMCs and
intermediate-aged OCs in metal-rich and metal-poor environments of the Local
Universe. These models are evolved with long-term, direct, relativistic
many-body computations incorporating state-of-the-art stellar-evolutionary and
remnant-formation models. Based on models of Local Universe constructed with
such model clusters, it is shown that YMCs and intermediate-aged OCs would
yield several 10s to 100s of LISA BBH sources at the current cosmic epoch with
GW frequency within $10^{-3}{\rm~Hz} - 10^{-1}{\rm~Hz}$ and
signal-to-noise-ratio (S/N) $>5$, assuming a mission lifetime of 5 or 10 years.
Such LISA BBHs would have a bimodal distribution in total mass, be generally
eccentric ($\lesssim0.7$), and typically have similar component masses although
mass-asymmetric systems are possible. Intrinsically, there would be 1000s of
present-day, LISA-detectable BBHs from YMCs and OCs. That way, YMCs and OCs
would provide a significant and the dominant contribution to the stellar-mass
BBH population detectable by LISA. A small fraction, $<5$%, of these BBHs would
undergo GR inspiral to make it to LIGO-Virgo GW frequency band and merge,
within the mission timespan; $<15$% would do so within twice the timespan.
