Using the Lebwohl-Lasher interaction for reciprocal local alignment, we present a comprehensive phase diagram for a dry, apolar, active nematic system using its stochastic off-lattice dynamics. The nematic-isotropic transition in this system is first-order and occurs alongside a fluctuation-dominated phase separation. Our phase diagram identifies three distinct regions based on activity and orientational noise relative to alignment strength: a homogeneous isotropic phase, a nematic phase with giant density fluctuations, and a coexistence region. Using mean-field analysis and hydrodynamic theory, we demonstrate that reciprocal interactions lead to a density fluctuation-induced first-order transition and derive a phase boundary consistent with numerical results. Quenching from the isotropic to nematic phase reveals coarsening dynamics where nematic ordering precedes particle clustering. Both the nematic and density fields exhibit similar scaling behaviors, exhibiting dynamic exponents zS ≈ 2.5 and zρ ≈ 2.34, consistently falling within the range of 2 and 3.