The morphological stability of lamellar eutectic coupled growth is investigated by means of quantitative three-dimensional phase-field simulations, both for a generic eutectic alloy with a symmetric phase diagram and for the transparent organic alloy carbontetrabromide-hexachloroethane. The instabilities that limit stable steady-state growth at large spacings are identified and compared to the instabilities known in thin samples. For all alloys and compositions investigated, the first instability to occur is a zigzag instability, which can saturate or lead to the breakup of the lamellae into rods or labyrinth structures, depending on the initial spacing and the volume fractions. The simulation results are in good agreement with recent experimental observations.