We study experimentally how synchronization emerges in a small network of delay-coupled lasers, as the coupling strength increases. Specifically, we optically couple three semiconductor lasers to each other via an external mirror. The system exhibits natural mismatches between its three elements, and is designed so that the coupling delays and strengths are non-uniform throughout the network. For weak coupling a cluster arises where two lasers synchronize their low-frequency dynamics; for stronger coupling all three lasers synchronize. A simple model gives good agreement with the experimental observations.