With the slowdown of process scaling and the advancement of packaging technologies, multi-chiplet GPUs have emerged as a highly promising architecture to improve the scalability of GPU performance further. Moreover, requiring adherence to atomicity and memory consistency models for shared data efficient synchronization is crucial to leverage the performance advantages of the multi-chiplet GPU architecture. However, the memory systems of multi-chiplet GPUs introduce deeper cache hierarchies and increased non-uniformity, both of which significantly exacerbate the overhead of synchronization. Specifically, acquire/release synchronization operations should invalidate/flush caches, an overhead that is significantly increased by the presence of additional cache level, and atomic operations for synchronization performed across chiplets are further impacted by the limited bandwidth of inter-chiplet links. To address these challenges, this paper proposes LRM-GPU to provide efficient synchronization support for multi-chiplet GPUs. In order to reduce the overhead caused by the additional cache level, LRM-GPU leverages lazy release consistency in multi-chiplet GPUs, whereby the additional level of cache only performs coherence actions when the ownership of synchronization variables changes between different chiplets. LRM-GPU also implements a directory in the last-level cache to track the synchronization variables. To mitigate the overhead of atomic operations for inter-chiplet synchronization under limited interchiplet bandwidth, LRM-GPU proposes an in-network synchronization atomic merging unit to merge atomic requests across chiplets, thereby reducing the inter-chiplet synchronization traffic of atomic operations. Experimental evaluation demonstrates that, compared with the MCM-GPU, LRM-GPU achieves an average speedup of 1.33×. Moreover, compared with the state-of-the-art work HMG, it also achieves the speedup of 1.22×, reduces 52% of inter-chiplet traffic, and reduces 32% of energy consumption on average.