Li-based half-Heusler alloys have attracted much attention due to their potential applications in optoelectronics and because they carry the possibility of exhibiting large magnetic moments for spintronic applications. Due to their similarities to metastable zinc blende half-metals, the half-Heusler alloys $beta$-LiMnZ (Z = N, P and Si) were systematically examined for their electric, magnetic and stability properties at optimized lattice constants and strained lattice constants that exhibit half-metallic properties. Other phases of the half-Heusler structure ($alpha$ and $gamma$) are also reported here, but they are unlikely to be grown. The magnetic moments of these stable Li-based alloys are expected to reach as high as 4 $mu_{mathrm{B}}$ per unit cell when Z = Si and 5 $mu_{mathrm{B}}$ per unit cell when Z = N and P, however the antiferromagnetic spin configuration is energetically favored when Z is a pnictogen. $beta$-LiMnSi at a lattice constant 14% larger than its equilibrium lattice constant is a promising half-metal for spintronic applications due to its large magnetic moment and vibrational stability. The modified Slater--Pauling rule for these alloys is determined. Finally, a plausible method for developing half-metallic Li$_x$MnZ at equilibrium, by tuning $x$, is investigated, but, unlike tetragonalization, this type of alloying introduces local structural changes that destroy the half-metallicity.
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