To elucidate the spin dynamics of La 2−x Sr x CuO 4 , which couples with the charge degree of freedom, the spin excitations spanning the characteristic energy (E cross ∼35-40 meV) are investigated for underdoped x = 0.10 and optimally doped (OP) x = 0.16 through inelastic neutron scattering measurements. Analysis based on two-component picture of high-quality data clarified the possible coexistence of uprightly standing incommensurate (IC) excitations with gapless commensurate (C) excitations in the energy-momentum space. The IC component weakens the intensity toward E cross with increasing energy transfer ( ω), whereas the C component strengthens at high-ω regions. The analysis results imply that the superposition of two components with a particular intensity balance forms an hourglass-shaped excitation in appearance. Furthermore, the temperature dependence of the intensity of each component exhibits different behaviors; the IC component disappears near the pseudo-gap temperature (T *) upon warming, whereas the C component is robust against temperature. These results suggest the itinerant electron spin nature and the localized magnetism of the parent La 2 CuO 4 in IC and C excitations, respectively, similar to the spin excitations in the OP YBa 2 Cu 3 O 6+δ and HgBa 2 CuO 4+δ with higher superconducting-transition temperatures.