The Level of Conceptual Interoperability Model (LCIM) is a widely used framework that represents inter-relationship among interoperability and composability of different information systems. Although this model has been successfully applied to various domains such as cybernetics and informatics, there are many challenges in directly adopting the model for blockchain-based systems. This paper identifies those challenges and proposes a new Level of Conceptual Interoperability Model for blockchain systems based on the original LCIM. We define five different levels of interoperability for blockchain-based systems and theoretically evaluate the level of interoperability (LOI) achieved by different blockchain networks. The evaluation outcomes show that there exists technical interoperability (Level 1) between Bitcoin and Ethereum networks, whereas Solana and Binance achieve pragmatic interoperability (Level 4) by conveying state changes with the Ethereum network and Polkadot achieve dynamic interoperability (level 5) by suitably conveying state changes within the ecosystem of its networks. We present case studies that demonstrate how the proposed LCIM for blockchain systems map various real-world applications to their respective levels.