The Laser Interferometer Space Antenna telescopes must exhibit an optical path length stability of p m/H z in the mHz observation band to meet mission requirements. The optical truss interferometer is a proposed method to aid in the ground testing of the telescopes, as well as a risk-mitigation plan for flight units. This consists of three Fabry-Perot cavities mounted to the telescope, which are used to monitor structural displacements. We have designed and developed a fiber-based cavity injection system that integrates fiber components, mode matching optics, and a cavity input mirror into a compact input stage. The input stages, paired with return mirror stages, can be mounted to the telescope to form optical truss cavities. We performed a thorough sensitivity analysis using various simulation methods to support the fabrication and assembly of three first-generation prototype cavities, each of which exhibited satisfactory performance based on our models.