Yes, there are a number of similarities. Both of us run an LSP and user nodes only connect to the LSP(s). But with Phoenix, the Lightning node runs on the mobile device, while with Lexe, the Lightning node runs inside an SGX enclave in the cloud; the mobile app is mostly used to remotely control the node (after the node and mobile app mutually authenticate each other of course). This difference in architecture allows us to help users receive payments when they're away from their phone.

Phoenix releases for Android first and iPhone second though, whereas this doesn't even have an Android option on the site ;_;

Also, Phoenix is based on Eclair (both written by the same company) whereas this is using LDK (could be relevant to what gets supported in the future)

I would also point out, that Phoenix's model is the LSP model which is also used by Breez and Mutiny. Its a good model imo, I like it.