Focused electron beam induced deposition (FEBID) is one of the few techniques that enables direct-write synthesis of free-standing 3D nanostructures. While the fabrication of simple architectures such as vertical or curving nanowires has been achieved by simple trial and error, processing complex 3D structures is not tractable with this approach. In part, this is due to the dynamic interplay between electron-solid interactions and the transient spatial distribution of absorbed precursor molecules on the solid surface. Here, we demonstrate the ability to controllably deposit 3D lattice structures at the micro/nanoscale, which have received recent interest owing to superior mechanical and optical properties. A hybrid Monte Carlo-continuum simulation is briefly overviewed, and subsequently FEBID experiments and simulations are directly compared. Finally, a 3D computer-aided design (CAD) program is introduced, which generates the beam parameters necessary for FEBID by both simulation and experiment. Using this approach, we demonstrate the fabrication of various 3D lattice structures using Pt-, Au-, and W-based precursors.