The biggest hurdle with phone LN wallets is that one cannot always be available to receive, 24/7. However, this rarely is necessary for most users, it's more of a business thing.
Phoenix and Breeze are indeed nodes on mobile and they work pretty good, while automating away some channel management with different methods.
Also wanted to mention Muun. Muun is a non-custodial wallet as well. With Muun, you have a unified (on-chain and LN) balance. If you scan an onchain QR, it just sends normally. If you scan a LN QR, it seems like it is sending via LN like a "Wallet of Satoshi" and it comes out of your one balance. But if it is non-custodial (unlike Wallet of Satoshi) how does it work without running a node on your phone?
Behind the scenes, it sends an on-chain transaction to Muun's headquarters (which it accepts without waiting for any confirmations). Muun then pays the LN invoice for you from their headquarters. This results in pretty high fees for a LN transaction (because it's actually charging for an on-chain one)(luckily, fees at the moment are around 50 cents.)
They were kind of secretive about this process because it can be exploited, since they accept a transaction without confirmations (fullRBF makes this vulnerability more dangerous.) For this reason and due to future expectations of a higher fee environment (like experienced in 2017-18) causing on-chain fees to be intolerably higher than LN fees, Muun is planning on changing the way they handle this.
Another interesting thing in the works is the Mutiny project. Citadel Dispatch episode 82 dives in (https://youtu.be/A1GLTQjVrlc).
They are attempting to run a full LN node/wallet in a browser. Apple's App Store has been moving in the direction of wanting their cut of all monetary exchanges. Recently Coinbase wallet has halted transfer of NFTs due to Apple wanting a cut of gas fees, which isn't really possible since Apple is only interested in receiving USD. Anyway, the Duopoly of Google's Play Store and Apple's App Store is a possible vector of censorship that may be circumvented by a browser wallet.
Another model is Zeus. It's a non-custodial mobile wallet that runs super fast with little resources by just connecting to an at-home Lightning Node. If someone has a node at home, this is the best route.
They are attempting to run a full LN node/wallet in a browser. Apple's App Store has been moving in the direction of wanting their cut of all monetary exchanges. Recently Coinbase wallet has halted transfer of NFTs due to Apple wanting a cut of gas fees, which isn't really possible since Apple is only interested in receiving USD. Anyway, the Duopoly of Google's Play Store and Apple's App Store is a possible vector of censorship that may be circumvented by a browser wallet.