We investigate the emission dynamics of mutually coupled nanolasers and predict ways to optimize their stability i.e. maximize their locking range. We find that tuning the cavity lifetime to the same order of magnitude as the dephasing time of the microscopic polarization yields optimal operation conditions which allow for wider tuning ranges than usually observed in conventional semiconductor lasers. The lasers are modeled by a Maxwell-Bloch type class-C laser model. For our analysis we analytically determine the steady state solutions, analyze the symmetries of the system and numerically characterize the emission dynamics via the underlying bifurcation structure. The polarization lifetime is found to be a crucial parameter which impacts the observed dynamics in the parameter space spanned by frequency detuning, coupling strength and coupling phase.