In this study, families of frozen orbits for a satellite revolving around the triaxial Moon are investigated. The Hamiltonian for this scenario is formulated, taking into account the lunar gravitational zonal harmonic coefficients up to  along with its most effective triaxiality factors, namely ,  and  Using canonical Lie transforms, the Hamiltonian undergoes an average process where short-term periodic elements are eliminated while retaining secular components up to the second order. New families of critical inclination roots are obtained; one of the roots lies in the vicinity of polar orbits, and the other is close to typical critical inclinations. This research investigates how variations in eccentricity, semi-major axis, and argument of periapsis affect these critical inclinations. A family of frozen orbits around the apsidal line and their graphical representation are revealed. To ensure such orbits, the argument of periapsis is solved. This establishes certain constraints when selecting the inclination that meets the criteria for the frozen argument of periapsis orbits. Significant perturbations in the critical inclination occur in high lunar orbits.