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.
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.
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.