The interplay between magnetic ordering and band topology has emerged as a fertile ground for discovering novel quantum states with profound implications for fundamental physics and next-generation electronics. Here, we theoretically predict a different type-III Weyl semi-half-metal (SHM) state in monolayer ${\mathrm{Li}}_2\mathrm{N}$, uniquely combining magnetic half-metallicity and type-III Weyl semimetal characteristics. First-principles calculations reveal a fully spin polarized and critically tilted Weyl cone around the Fermi level in monolayer ${\mathrm{Li}}_2\mathrm{N}$, driven by $p$-orbital ferromagnetism. This arises from the symmetry-protected band crossing between a partially flat valence band and a highly dispersive conduction band, leading to type-III Weyl fermions with strong transport anisotropy. A low-energy $k·p$ Hamiltonian is constructed and corresponding nontrivial edge states are uncovered to capture the topological nature of ${\mathrm{Li}}_2\mathrm{N}$. Notably, this Weyl SHM phase remains robust under biaxial strain ranging from $-2\%$ to $4\%$, with an ideal type-III Weyl fermion emerging alongside a linelike ergodic surface emerging at $3.7\%$ strain, offering a promising platform for exploring correlated electronic phenomena. Our results establish ${\mathrm{Li}}_2\mathrm{N}$ as a viable candidate for realizing exotic type-III Weyl SHM states and open an avenue for exploring the intricate interplay among magnetism, topology, and flat-band physics.

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• Electronic structure
• First-principles calculations
• Topological materials
• 2-dimensional systems
• Half-metals