The study investigates the relaxation of a three-component dusty plasma in the lunar atmosphere. By employing Amp & egrave;re's law with momentum balance equation of the plasma species, which includes an electron, a positive ion, and a negatively charged dust particle, a Triple Beltrami (TB) state is obtained. This TB state is characterized by three scale parameters, which may be real or complex. The Cartesian coordinate geometry is employed to analyze the magnetic field profiles. The Beltrami parameters, mass of negative charged dust particulates and density variations at different height and angle have a significant impact on the magnetic properties of the self-organized structures in lunar atmosphere. The study reveals that all scale parameters associated with diamagnetic structures are real and complex, while all scale parameters for paramagnetic structures are real. It has been shown that the magnetic field, along with its complex conjugate and real part, increases with height and angle, and only diamagnetic structures are formed in the lunar atmosphere. The findings of this study should help to explain relaxed structures found in other astronomical objects and in lab settings including negatively charged dust particles, ions, and electrons.