  It has been shown in the past, that the six Doppler data streams obtained
LISA configuration can be combined by appropriately delaying the data streams
for cancelling the laser frequency noise. Raw laser noise is several orders of
magnitude above the other noises and thus it is essential to bring it down to
the level of shot, acceleration noises. A rigorous and systematic formalism
using the techniques of computational commutative algebra was developed which
generates all the data combinations cancelling the laser frequency noise. The
relevant data combinations form a first module of syzygies. In this paper we
use this formalism for optimisation of the LISA sensitivity by analysing the
noise and signal covariance matrices. The signal covariance matrix, averaged
over polarisations and directions, is calculated for binaries whose frequency
changes at most adiabatically. We then present the extremal SNR curves for all
the data combinations in the module. They correspond to the eigenvectors of the
noise and signal covariance matrices. We construct LISA `network' SNR by
combining the outputs of the eigenvectors which improves the LISA sensitivity
substantially. The maximum SNR curve can yield an improvement upto 70 % over
the Michelson, mainly at high frequencies, while the improvement using the
network SNR ranges from 40 % to over 100 %. Finally, we describe a simple toy
model, in which LISA rotates in a plane. In this analysis, we estimate the
improvement in the LISA sensitivity, if one switches from one data combination
to another as it rotates. Here the improvement in sensitivity, if one switches
optimally over three cyclic data combinations of the eigenvector is about 55 %
on an average over the LISA band-width. The corresponding SNR improvement is 60
%, if one maximises over the module.
