Not sure if you’re asking the interoperability between layer-1 and layer-2 or between two layer-2 protocols?
The layer-2 projects we see today are not mature, most of them are in prototype phase and is highly coupled to a certain blockchain. A layer-2 project may add support for multiple blockchains and become layer-1 agnostic, or some 3rd-party will clone it onto a different blockchain.
The interoperability between layer-2 protocols is an important but non-urgent problem because we don’t even have a mature layer-2 project yet. It’s a problem on our radar too. There’re some common things we need for this two interoperability problems, such as networking protocol. However the interoperability between layer-2 is more trickier than the interoperability between layer-1 and layer-2, because we don’t know what will a global layer-2 network look like yet - what’s the role of different layer-2 protocols, e.g. channels and chains, in this layer-2 network? How do channels interact with chains?