  A phase-locking configuration for LISA is proposed that provides a
significantly simpler mode of operation. The scheme provides one Sagnac signal
readout inherently insensitive to laser frequency noise and optical bench
motion for a non-rotating LISA array. This Sagnac output is also insensitive to
clock noise, requires no time shifting of data, nor absolute arm length
knowledge. As all measurements are made at one spacecraft, neither clock
synchronization nor exchange of phase information between spacecraft is
required. The phase-locking configuration provides these advantages for only
one Sagnac variable yet retains compatibility with the baseline approach for
obtaining the other TDI variables. The orbital motion of the LISA constellation
is shown to produce a 14 km path length difference between the
counter-propagating beams in the Sagnac interferometer. With this length
difference a laser frequency noise spectral density of 1 Hz/$\sqrt{\rm Hz}$
would consume the entire optical path noise budget of the Sagnac variables. A
significant improvement of laser frequency stability (currently at 30
Hz/$\sqrt{\rm Hz}$) would be needed for full-sensitivity LISA operation in the
Sagnac mode. Alternatively, an additional level of time-delay processing could
be applied to remove the laser frequency noise. The new time-delayed
combinations of the phase measurements are presented.
