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 N${}_2^{+}$ lasing at 391 nm, corresponding to the $B^2{\Sigma }_u^{+}(v\prime =0)\to X^2{\Sigma }_g^{+}(v=0)$ transition. By solving the open-system density matrix in a rovibronic-state basis and Maxwell-Bloch equations, we examine both the formation of the 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 $X^2{\Sigma }_g^{+}(v=0)$ and $B^2{\Sigma }_u^{+}(v\prime =0)$ 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 N${}_2^{+}$ air lasing and highlight its potential as a tunable parameter for controlling lasing dynamics.