A resonant inelastic x-ray scattering study of overdamped spin excitations in slightly underdoped La2-xSrxCuO4 (LSCO) with x = 0.12 and 0.145 is presented. Three high-symmetry directions have been investigated: (1) the antinodal (0,0) -> (½,0), (2) the nodal (0,0) -> (¼, ¼), and (3) the zone-boundary direction (½,0) -> (¼, ¼) connecting these two. The overdamped excitations exhibit strong dispersions along (1) and (3), whereas a much more modest dispersion is found along (2). This is in strong contrast to the undoped compound La2CuO4 (LCO) for which the strongest dispersions are found along (1) and (2). The t - t' - t'' - U Hubbard model used to explain the excitation spectrum of LCO predicts-for constant U/t-that the dispersion along (3) scales with (t'/ t)2. However, the diagonal hopping t' extracted on LSCO using single-band models is low (t'/t ∼ -0.16) and decreasing with doping. We therefore invoked a two-orbital (dx2-y2 and dz2) model which implies that t' is enhanced. This effect acts to enhance the zone-boundary dispersion within the Hubbard model. We thus conclude that hybridization of dx2-y2 and dz2 states has a significant impact on the zone-boundary dispersion in LSCO.