What does "post-quantum" actually mean for a Bitcoin L2 when settlement still happens on a non-PQ L1?

The recent discussion focuses on the advancements in blockchain security, specifically addressing the post-quantum cryptography implications for Bitcoin's Lightning Network. The detailed examination of these issues is available through the document found at PQLN, which provides insights into how the network can enhance its resistance against potential quantum computing threats. This resource is instrumental for those interested in understanding the intersection of emerging technologies and cryptocurrency security frameworks, offering a deep dive into the technical strategies that could be employed to safeguard digital assets in a new era of computing capabilities.