Verifying the integrity of IoT data in cloud-based IoT architectures is crucial for building reliable IoT applications. Traditional data integrity verification methods rely on a Trusted Third Party (TTP) that has issues of risk and operational cost by centralization. Distributed Ledger Technology (DLT) has a high potential to verify IoT data integrity and overcome the problems with TTPs. However, the existing DLTs have low transaction throughput, high computational and storage overhead, and are unsuitable for IoT environments, where a massive scale of data is generated. Recently, Directed Acyclic Graph (DAG) based DLTs have been proposed to address the low transaction throughput of linear DLTs. However, the integration of IoT Gateways (GWs) into the peer to peer (P2P) DLT network is challenging because of their low storage and computational capacity. This paper proposes Lightweight and Scalable DAG based distributed ledger for IoT (LSDI) that can work with resource-constrained IoT GWs to provide fast and scalable IoT data integrity verification. LSDI uses two key techniques: Pruning and Clustering, to reduce 1) storage overhead in IoT GWs by removing sufficiently old transactions, and 2) computational overhead of IoT GWs by partitioning a large P2P network into smaller P2P networks. The evaluation results of the proof of concept implementation showed that the proposed LSDI system achieves high transaction throughput and scalability while efficiently managing storage and computation overhead of the IoT GWs. © 2021 IEEE.