  The Large Synoptic Survey Telescope (LSST) will provide for unbiased sampling
of variability properties of objects with $r$ mag $<$ 24. This should allow for
those objects whose variations reveal their orbital periods ($P_{orb}$), such
as low mass X-ray binaries (LMXBs) and related objects, to be examined in much
greater detail and with uniform systematic sampling. However, the baseline LSST
observing strategy has temporal sampling that is not optimised for such work in
the Galaxy. Here we assess four candidate observing strategies for measurement
of $P_{orb}$ in the range 10 minutes to 50 days. We simulate multi-filter
quiescent LMXB lightcurves including ellipsoidal modulation and stochastic
flaring, and then sample these using LSST's operations simulator (OpSim) over
the (mag, $P_{orb}$) parameter space, and over five sightlines sampling a range
of possible reddening values. The percentage of simulated parameter space with
correctly returned periods ranges from $\sim$23 %, for the current baseline
strategy, to $\sim$70 % for the two simulated specialist strategies. Convolving
these results with a $P_{orb}$ distribution, a modelled Galactic spatial
distribution and reddening maps, we conservatively estimate that the most
recent version of the LSST baseline strategy will allow $P_{orb}$ determination
for $\sim$18 % of the Milky Way's LMXB population, whereas strategies that do
not reduce observations of the Galactic Plane can improve this dramatically to
$\sim$32 %. This increase would allow characterisation of the full binary
population by breaking degeneracies between suggested $P_{orb}$ distributions
in the literature. Our results can be used in the ongoing assessment of the
effectiveness of various potential cadencing strategies.
