${\mathrm{N}}_2^{+}$ air lasing has attracted considerable attention owing to its promising applications in remote sensing and the ongoing debates regarding its underlying generation mechanisms. Here, we present a theoretical investigation of the molecular rotational effects in ${\mathrm{N}}_2^{+}$ lasing at 391 nm, corresponding to the $B^2{\mathrm{\Sigma }}_u^{+}(v^{\prime }=0)\to X^2{\mathrm{\Sigma }}_g^{+}(v=0)$ transition. By solving the open-system density matrix in a rovibronic-state basis and Maxwell-Bloch equations, we examine both the formation of the ${\mathrm{N}}_2^{+}$ gain medium induced by a femtosecond pump pulse and the subsequent seed-induced amplification during propagation. During the pump stage, rotational dynamics are found to significantly modify the angle-dependent populations of ionic vibrational-electronic states within just a few tens of femtoseconds. Furthermore, ionization-produced rotational coherences substantially enhance the population inversion between the $X^2{\mathrm{\Sigma }}_g^{+}(v=0)$ and $B^2{\mathrm{\Sigma }}_u^{+}(v^{\prime }=0)$ states. In the subsequent seed-induced propagation stage, lasing amplification is driven by the joint action of population inversion and rotational coherence. These findings reveal the crucial role of molecular rotation in ${\mathrm{N}}_2^{+}$ air lasing and highlight its potential as a tunable parameter for controlling lasing dynamics.

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• Light-matter interaction
• Rotational states