By integrating edge computing with blockchain technology, traceable and immutable services can be provided to address the distrust issue between edge devices. However, the contradiction between the computing and storage requirements of blockchain deployment and the constrained resources of edge devices is the greatest obstacle standing in the way. This makes edge devices have to consume expensive costs to deploy a blockchain system for trusted collaboration. To address the above problem, this article proposes a resource-efficient blockchain framework for edge computing. First, we propose a cloud-edge collaboration consensus protocol called the Proof-of-Lottery (PoL) that completely offloads the computing requirement of consensus protocol execution from edge devices to the cloud. By introducing double-chain structure and dynamic difficulty target mechanism, PoL can significantly improve the throughput and latency of the blockchain transaction while remains decentralization and security. Then, the framework division mechanism based on edge-terminal consensus zone (ETCZ) is proposed to decrease the minimum storage requirement for resource constrained edge devices. The multi-ETCZ PoL protocol is also designed for consensus in the multi-ETCZ blockchain framework. Finally, controlled experiments are tested to demonstrate that our framework can significantly reduce the resource requirements for edge devices on blockchain deployment while achieving high-throughput and low-latency services.