This paper considers synchronization of Lur’e systems under a dynamic event-triggered framework. To facilitate the study, a novel time-varying sampled-data-related dynamic event-triggered control (ETC) related to fully discrete local information is proposed, which does not require continuous communication among nodes and naturally avoids Zeno behavior. By using the Halanay inequality, a number of sufficient criteria to achieve leader-following synchronization are derived, from which the allowable sampling interval can be calculated. In addition, the introduction of dynamic parameters in event-triggered condition shows better performance in reducing the event-triggered number, since the existing of a negative term in event-triggered condition slows down the rapid growth of triggering threshold. Further, heterogeneous Lur’e networks are investigated. By taking advantage of the boundedness of leaders, quasi-synchronization can be guaranteed in heterogeneous Lur’e networks, which makes the conclusions more general. At last, to show the effectiveness of the derived sampled-data-based dynamic ETC mechanism in both homogeneous and heterogeneous Lur’e networks separately, two simulation examples are presented.