Ok, found the answer to my question here: https://10101.substack.com/p/noncustodial-trading-with-10101
Lightning doesn't currently support DLCs out of the box. This means that we need to make changes to a regular Lightning node in order to make this happen. This is exactly what we started doing for our project for the Legends of Lightning tournament organised by BOLT.FUN. Under the name of 10101, we built a proof-of-concept mobile Lightning wallet, with CFD trading as its flagship feature.