Muun uses submarine swaps with chained HTLCs in zero-conf on-chain transactions (either 0 or both get confirmed, so it's “probably” safe). They run LN node in the middle to handle actual connection to other LN wallets, and handle all channels & liquidity. Your Muun corn are always on-chain, not on LN.
Phoenix is a proper LN node on mobile, but it works by only connecting to ACINQ LN nodes so they can still manage channels and liquidity. Phoenix corn are on LN proper.
If you want to manage own channels and liquidity, you need to run CLN or LND on a computer and manage via CLI, web GUI app, or mobile app (Zeus).