The expansion of the blockchain scale puts higher demands on the parallel performance of distributed consistency algorithms. In recent years, protocols represented by Tusk have driven the development of Byzantine fault tolerant (BFT) protocols by integrating directed acyclic graph (DAG). These protocols divide consensus into communication layer and ordering layer, enabling parallel execution of block broadcasting and agreements in the expectation of increased throughput. However, traditional DAG-based BFT protocols require nodes to deliver a sufficient number of peer broadcast blocks before broadcasting a new block, which actually limits parallel performance. In addition, they uses the leader block to commit all blocks, which is unfair to slow progressing nodes as their blocks are excluded by consensus. To address these challenges, we propose LSDBFT, a novel asynchronous BFT protocol that redefines the communication and ordering layers for improved scalability and fairness. The communication layer of LSDBFT employs a loose DAG structure where each node broadcasts blocks at its own pace through sequential provable broadcasts (PBs), eliminating the cross-node synchronization delays inherent in the traditional DAG reference mechanism. The ordering layer leverages an asynchronous binary agreement (ABA) protocol to establish a fair total ordering of blocks, ensuring equitable commitment even for slow-progressing nodes. Unlike leader-centric approaches, LSDBFT’s ABA-driven mechanism avoids favoring specific nodes, enhancing decentralization. We prove the security of the LSDBFT protocol and verify its efficiency through experimental evaluation. In conclusion, LSDBFT advances the application of distributed consensus algorithms in high-throughput environments by harmonizing parallelism with fair block ordering.