We present detailed numerical studies of the dynamics of three semiconductor lasers when interacting in a linear chain through the mutual injection of their optical fields. In particular, we focus on the synchronization properties of the coupling-induced dynamics and the role of the delay in the interaction between the lasers. The recently experimentally and numerically demonstrated zero-lag synchronization in Ref.[1] between the outer lasers in the chain is here further analyzed in detail along with a study of the robustness of this phenomenon. In addition, the propagation properties of perturbing pulses and of harmonic modulation are discussed.