LZ is a next-generation dark matter search experiment designed to significantly extend our sensitivity to WIMP dark matter candidates. At the core of the LZ detector is a dual-phase xenon time projection chamber (TPC) with a 7-ton active mass. To observe signals from low-energy nuclear recoils, including WIMP-xenon scatters, four custom-woven wire-mesh grids of 1.5m diameter establish strong electric fields in the TPC to drift ionization electrons across the volume and extract them from the liquid surface. As a result of the high electric fields, dielectric breakdown between high voltage surfaces and spurious electron emission from regions of high surface fields are major concerns. To mitigate these risks, an R&D program exploring design geometry in high field regions, cleanliness procedures, and surface treatments has been carried out using a comprehensive suite of three mid-scale dual- and single-phase xenon detectors. These proceedings will summarize the design and construction of the LZ grids, and several aspects of the high voltage performance seen in the testing program.