I think you're confusing things. At an inclination of ~63.4 degrees, the rotation of the orbit ellipse about the h vector is zero, in other words the argument of the perigee does not change with time. But the orbit plane does not remain fixed in inertial space, it regresses westward around the ECI z-axis at a rate depending on the semimajor axis and eccentricity (regression of the ascending node). The 63.4 degree figure applies only to earth orbits, since every planet has its own nonspherical mass properties, of course.
In any case, the OP wants to be in the Lunar plane, which is only about 28-29 degrees. 63.4 is far away from that. At this inclination, the argument of perigee will move with respect to time due to nonspherical earth (J2), but if your orbit is near circular that's not a problem. The problem is staying in the lunar plane, which as you said, is possible only with periodic propulsive maneuvers. The reason for this is both J2 effect and third body gravity from the sun and the moon.
It should be posible to choose an orbit that will remain "moon syncronous", that is, the angle between the orbit plane and the moon's orbit plane will remain constant, but I don't think you can make it zero.