The high latency and low throughput of blockchain protocols constitute one of the fundamental barriers for their wider adoption. Overlay protocols, notably the lightning network, have been touted as the most viable direction for rectifying this in practice. In this work we present for the first time a full formalisation and security analysis of the lightning network in the (global) universal composition setting that leverages a global ledger functionality, for which realisability by the Bitcoin blockchain protocol has been demonstrated in previous work [Badertscher et al., Crypto’17]. As a result, our treatment delineates exactly how the security guarantees of the protocol depend on the properties of the underlying ledger and the frequent availability of the protocol participants. Moreover, we provide a complete and modular description of the core of the lightning protocol that highlights precisely its dependency to underlying basic cryptographic primitives such as igital signatures, pseudorandom functions, identity-based signatures and a less common two-party primitive, which we term a combined digital signature, that were originally hidden within the lightning protocol’s implementation.