Lateral inhibition resulting from a double-negative feedback loop underlies the assignment of different fates to cells in many developmental processes. Previous studies have shown that the presence of time delays in models of lateral inhibition can result in significant oscillatory transients before patterned steady states are reached. We study the impact of local feedback loops in a model of lateral inhibition based on the Notch signalling pathway, elucidating the roles of intracellular and intercellular delays in controlling the overall system behaviour. The model exhibits both in-phase and out-of-phase oscillatory modes, and oscillation death. Interactions between oscillatory modes can generate complex behaviours such as intermittent oscillations. Our results provide a framework for exploring the recent observation of transient Notch pathway oscillations during fate assignment in vertebrate neurogenesis. ; Comment: 17 figures, to appear in Phys Rev E