We report on the design, implementation, and characterization of fully digital control loops for laser frequency stabilization, differential phase-locking, and performance optimization of the optical metrology system on-board the LISA Pathfinder space mission. The optical metrology system consists of a laser with modulator, four Mach-Zehnder interferometers, a phase-meter and a digital processing unit for data analysis. The digital loop design has the advantage of easy and flexible controller implementation and loop calibration, automated and flexible locking and resetting, and improved performance over analog circuitry. Using the practical ability of our system to modulate the laser frequency allows us to accurately determine the open-loop transfer function and other system properties. Various noise sources and their impact on system performance are investigated in detail.