In pursuit of new lithium-rich phases and potential electrides within the Li N phase diagram, we explore theoretically the ground-state structures and electronic properties of Li4N at P = 1 atm. Crystal structure exploration methods based on particle swarm optimization and evolutionary algorithms led to 25 distinct structures, including 23 dynamically stable structures, all quite close to each other in energy, but not in detailed structure. Several additional phases were obtained by following the imaginary phonon modes found in low-energy structures, as well as structures constructed to simulate segregation into Li and Li3N. The candidate Li4N structures all contain NLin polyhedra, with n = 6-9. They may be dassified into three types, depending on their structural dimensionality: NLin extended polyhedral slabs joined by an elemental Li layer (type a), similar structures, but without the Li layer (type b), and three-dimensionally interconnected NLin polyhedra without any layering (type c). We investigate the electride nature of these structures using the electron localization function and partial charge density around the Fermi level. All of the structures can be characterized as electrides, but they differ in electronic dimensionality. Type-a and type-b structures may be classified as two-dimensional (2-D) electrides, while type-c structures emerge quite varied, as 0-D, 2-D, or 3-D. The calculated structural variety (as well as detailed models for amorphous and liquid Li4N) points to potential amorphous character and likely ionic conductivity in the material.