The mixed alkali silicate glasses doped 0.1 mol% $Fe_2O_3$ are fabricated for studying the effect of transition metal oxides, which is related to the $Li^-$ ion movement in Magic-Angle-Spinning NMR. We have investigated the spin-lattice relaxation times in the room temperature and measured the $^7Li$ MAS-NMR spectrum with temperature. When the $Fe_2O_3$ oxides are added in alkali silicate glasses, the width of spectrum is changed a little but the line shape is hardly varied. For this reason, we can think that the mixed alkali effects are shown sufficiently in the spin-spin relaxation processes. However, it is not mixed alkali effects in this case. The activation energy of $Li^-$ ions are diminished in mixed alkali glasses. From the analysis of $Li^-$ diffusion environment, spin-lattice relaxation time and the nuclear magnetization, it is confirmed that the alkali mixed effects are not shown in $^7Li$ spin-lattice relaxation processes.