The LISA mission will form the equivalent of a Michelson interferometric beat signal from the 1064nm laser beams traversing the inter-spacecraft arms. The design gravitational wave sensitivity requires measurement of round trip path differences for each detector to be about 10 pm/square rootHz over a frequency range from 10-4 to 10-1 Hz. Thus LISA's phasemeter must measure the beat signal phase to 10-5 cycle/square rootHz at 1mHz. Doppler shifts between spacecraft in their orbits are expected to range from 1 to 15 MHz. Phase measurement using the digital phase-locked loop approach incorporated in a modified TurboRogue GPS receiver has been investigated in this study. It is found that only resolution in the range of 10-4 to 10-3 cycle/square rootHz at 1 mHz is achievable with this hardware. Abrupt fluctuations in the phase measurement at the millicycle level are responsible for the limitation.