We present the effects of temperature (between 10 K and 298 K) and of hole concentration on the frequency and intensity of characteristic phonons in polycrystalline $La_2CuO_4-related$ compounds using FT-IR spectros-copy. The influences of the concentration of carrier doped on the phonon modes are prominent in the IR spectra of $La_2CuO_4-related$ compounds. For $La_2-xSrxCuO_4({chi}=$ 0.00, 0.03, 0.07, 0.10, and 0.15) and electrochemically (or chemically) oxidized $La_2CuO_4$, the intensities of the transverse oxygen mode around 680cm $-^1$ which cor-responds mainly to Cu-O(1) stretching vibration in the basal plane of CuO6 octahedron, are decreased and dis-appeared depending on the Sr-substitution rate and the amount of excess oxygen, while the longitudinal oxygen mode around 510 cm $-^1$ corresponding to the Cu-O(2) stretching in the basal plane of CuO6 octahedron are near-ly invariable. In particular, after two cycles of cooling-heating between 10 K and 298 K for these sample, the phonons around 680 cm $-^1$ are blue shif 13-15 cm $-^1$, while the phonons around 510 cm $-^1$ are nearly constant. The introduction of the charge carrier by doping would give rise to the small contraction of CuO6 oc-tahedron as Cu $^3+$ requires a smaller site than Cu $^2+$, which results in the shortening of the Cu-O(1) bond length and Cu-O(2) bond length with the increased La-O(2) bond length. These results in the frequency shift of the characteristic phonons. The IR spectra of $La_2Li0.5Cu0.5O_4$ which exhibits an insulator behavior despite the $Cu^3+$ of nearly 100%, corroborate our IR interpretations. The mode around 710 cm $-^1$ corresponding to Cu-O(1) stretching vibration is still strongly remained even at low temperature (10 K). Thus, we conclude that the con-duction electrons formed within $CuO_2$ planes of $La_2CuO_4-related$ superconductors screen more effectively the transverse oxygen breathing mode around 680 $cm-^1$ depending on the concentration of the doped charge carrier in $La_2CuO_4-related$ compounds, which might use as a superconductivity probe.