This paper examines the problem of master-slave synchronization control for chaotic Lur'e systems (CLS) under sampled-data conditions. Initially, a two-sided looped Lyapunov function is constructed by fully leveraging the system characteristics and information regarding the sampling mode. Subsequently, based on the Lyapunov stability theory and using the integral inequality of free matrices, we establish the stability criteria for the synchronization error system of CLS. Utilizing these conditions, we compute the sampling controller gains through an enhanced iterative conditioned cone complementarity linearization iteration algorithm, thereby achieving synchronization of the master-slave system over more extended sampling periods. Ultimately, numerical examples are presented to demonstrate that the proposed method outperforms existing approaches documented in the literature.