On the basis of perturbation theory in fine structure constant alpha and the ratio of electron to muon masses we calculate one-loop vacuum polarization, electron vertex corrections, nuclear structure and recoil corrections to hyperfine splitting of the ground state in muonic lithium ions (μ e^6_3Li)^+ and (μ e ^7_3Li)^+. We obtain total results for the ground state small hyperfine splittings in (μ e ^6_3Li)^+ Δν_1=21572.16 MHz and Δν_2=14152.56 MHz and in (μ e ^7_3Li)^+ Δν_1=21733.06 MHz and

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... 2=13994.35 MHz which can be considered as a reliable estimate for a comparison with future experimental data.