The Lightning Network is usually implemented as a Layer-2, sitting on top of a Layer-1. Lightning is currently implemented for the layer-1 blockchains of Bitcoin and Litecoin. BOLT compliant implementations (e.g. Lnd , Eclair) use On-chain transactions and do not have their only coin(s).
In contrast to the typical Lightning Network implementation exist other implementations such as Liquid by Blockstream that implement Lightning functionality as a Side-chain. Being a side chain, these implementations have their own coins and can even create a multitude of their own tokens.
See also Cross-chain implementations.