We present a detailed concept for the realization of the LISA optical metrology subsystem, which employs heterodyne interferometry in a so-called "strap-down" architecture to accomplish a highly sensitive detection of gravity-wave induced displacements of dedicated mass references within the payload of the three LISA satellites. A frequency swap between transmitted and local reference beam is introduced to minimize the impact of stray light on the measurement sensitivity. The performance of the system is demonstrated by first optical modeling.