https://muun.com/ claims it has a wallet that does not rely on backups.
Here: https://blog.muun.com/why-not-just-a-mnemonic/ it says
Muun is a multisig wallet with lightning support, so backing up a mnemonic alone would mean your bitcoin could be easily frozen. Self-custodianship is at the core of everything we do, so this wasn't acceptable. We built an Emergency Kit that gives you full self-custody of your money when combined with your Recovery Code[6].
Your Emergency Kit is a PDF document with the information and instructions needed to find and spend your funds independently. No need to brute-force any missing data. Everything is there, including your private keys and output descriptors[7].
Your private keys are securely encrypted with your Recovery Code. This makes your Emergency Kit harmless by itself: you can keep multiple copies, and you can even store it safely on the cloud.
How can it, however, keep track of the state of my lightning wallet? If I use it to only spend, then there's no problem. However, if I receive more than I spend, it's of my interest to save the transaction state so I can propagate it when I want to close the channel.
I don't see how this emergency recovery kit can help me recovering the state.