The semi-classical method for determining the rate coefficients of the chemi-ionization processes in slow non-symmetric atom-Rydberg atom collisions is applied to the Li*(n) + Na case. Calculated rate coefficients are compared with the existing experimental data from the literature. Obtained results have confirmed that resonant mechanism of non-elastic processes in atom-Rydberg atom collisions are fully applicable to non-symmetric chemi-ionization processes. The rate coefficients of such processes in Li*(n) + Na collisions are determined in the regions of principal quantum number and temperature 4 ≤ n ≤ 20 and 700 K ≤ T ≤ 1100 K which can be of interest for possible further experiments. Also, the potential curves of several lowest Σ states of the molecular ion LiNa⁺, as well as the values of the square of dipole matrix element for the transition between X²Σ⁺- and A²Σ⁺-states, are presented in this paper.