Our previous study of the magnetic susceptibility, χ, on zero-field and field cooling and magnetization-hysteresis-loop (MHL) for La2-xSrxCuO4 (LSCO) single crystals with x = 0.178 – 0.261 has suggested that a microscopic phase separation into superconducting (SC) and normal-state regions takes place in the overdoped regime of LSCO. In order to clarify the onset hole-concentration where the microscopic phase separation appears, we have carried out χ measurements on zero-field and field cooling and MHL measurements for LSCO single crystals with x = 0.125 and 0.147. From the χ measurements in a low magnetic field on field cooling, absolute values of χ at 2 K, |χ2k|, in x = 0.125 and 0.147 have been found to be smaller than that of x = 0.178, which can be understood in terms of the vortex-pinning effect around twin boundaries in a crystal. Neither two-step SC transition in χ vs- T in a moderate field on zero-field cooling nor second magnetization peak in MHL has been observed in x = 0.125, while both characteristics have been observed in x = 0.147. These results imply no enhancement of the vortex pinning in a moderate field-range and therefore suggest the existence of a homogeneous superconducting state in x = 0.125. Accordingly, it is concluded that the onset hole-concentration of the microscopic phase separation is located between x = 0.125 and 0.147.