This study presents the calculation of stretching vibrational frequencies for the triatomic molecule dichlorine monoxide (Cl₂O), explicitly focusing on the fourth, fifth, and sixth overtones. Using a Lie algebraic framework, we provide a detailed mathematical modeling approach to predict these higher overtone frequencies accurately. The results demonstrate the effectiveness of the Lie algebraic method in capturing the complex vibrational behavior of Cl₂O, offering valuable insights into its vibrational spectra.