Thanks. As for my exact question, I've found the answer: If ACINQ disappears, you have to go to your Phoenix wallet (don't uninstall it until you've recovered your funds!) and use the "force close channels" feature. After 5 days your channels will be closed and the funds will appear in your on-chain wallet, which you can restore using your 12 word seed phrase.

All that assuming the mobile app does what it says it does (and it's open source, so has many people's eyes on it). The app stores static channel backups, which allow you to close the channels.