  High Li abundances have been reported in the late type secondaries of five
soft X-ray transients (SXTs), V404 Cyg, A0620-00, GS2000+25, Nova Mus 1991, and
Cen X-4. Since Li is likely to be depleted in stars of this type, the origin of
the Li is puzzling. Li has not been seen in similar secondaries of cataclysmic
variables, which suggests that the high Li abundance is not due to an anomalous
suppression of Li depletion in close binaries. SXTs in the quiescent state have
hot advection-dominated accretion flows (ADAFs) in which the ions are
essentially at virial temperature. At such temperatures, Li production via
$\alpha-\alpha$ spallation is possible. We show that quiescent SXTs can produce
sufficient Li via spallation to explain the observations in V404 Cyg, A0620-00,
GS2000+25, and Nova Mus 1991. Depending on the Li depletion time scale in the
secondary, which may range between $10^7-10^9$ yr, the model requires $\sim
10^{-4}-10^{-6}$ of the accreted mass to be intercepted by the secondary after
undergoing Li production and being ejected. In the case of Cen X-4, we can
explain the observed Li only if the mass accretion rate is $\sim 10^{-3}$ times
the Eddington rate and if there is enhanced ejection due to a propeller effect.
We discuss possible observational tests of this proposal. Li production during
outbursts could be quite important and may even dominate over the production
during quiescence, but the estimate of the Li yield is uncertain. We calculate
the expected luminosity in gamma-ray lines due to the production of excited Li
and Be nuclei, but conclude that the line cannot be detected with current
instruments.
