  It was shown in a previous work that the data combinations canceling laser
frequency noise constitute a module - the module of syzygies. The cancellation
of laser frequency noise is crucial for obtaining the requisite sensitivity for
LISA. In this work we show how the sensitivity of LISA can be optimised for a
monochromatic source - a compact binary - whose direction is known, by using
appropriate data combinations in the module. A stationary source in the
barycentric frame appears to move in the LISA frame and our strategy consists
of "coherently tracking" the source by appropriately "switching" the data
combinations so that they remain optimal at all times. Assuming that the
polarisation of the source is not known, we average the signal over the
polarisations. We find that the best statistic is the `network' statistic, in
which case LISA can be construed of as two independent detectors. We compare
our results with the Michelson combination, which has been used for obtaining
the standard sensitivity curve for LISA, and with the observable obtained by
optimally switching the three Michelson combinations. We find that for sources
lying in the ecliptic plane the improvement in SNR increases from 34% at low
frequencies to nearly 90% at around 20 mHz. Finally we present the
signal-to-noise ratios for some known binaries in our galaxy. We also show
that, if at low frequencies SNRs of both polarisations can be measured, the
inclination angle of the plane of the orbit of the binary can be estimated.
