We report here on a local spin valve effect observed unambiguously in lateral all-semiconductor all-electrical spin injection devices, employing p(+)-(Ga,Mn)As/n(+)-GaAs Esaki diode structures as spin aligning contacts. We discuss the observed local spin-valve signal as a result of the interplay between spin-transport-related contribution and the tunneling anisotropic magnetoresistance of the magnetic contacts. The magnitude of the spin-related magnetoresistance change is equal to 30 Omega which is twice the magnitude of the measured non-local signal. Copyright 2011 Author(s). This article is distributed under a Creative Commons Attribution 3.0 Unported License. [doi:10.1063/1.3591397]