We report on our theoretical analysis of the hyperfine splitting in the spectra of the 1 ³Δ _g, 2 ³Π _g, and 3 ³Σ _g ⁺ triplet states of ⁶Li ⁷Li, which were experimentally observed in 2002 (Li et al.) by means of Perturbation Facilitated Optical-Optical Double Resonance (PFOODR) spectroscopy. In our previous work, both homonuclear and heteronuclear molecules were analyzed. However, in this work, we theoretically investigate an isotope-substituted homonuclear molecule for the first time and demonstrate the application of our approach to this case. In our model, we reproduce the major stages of the excitation–de-excitation schemes by considering the mixed nature of the intermediate A ¹Σ _u ⁺∼b ³Π _Ωu singlet–triplet states, whereby the three components of the Ω=0,1,2 basis states might contribute to the hyperfine splitting. We compute the contributions from all components of the mixed states. We present physical models for all triplet states under study, along with the obtained parameters of the analyzed molecular system and the simulation results. Additionally, we describe the principal steps of the computational algorithm in detail.