Zeus isn't a wallet, it's only a UX to whichever wallet you have. It's common to use Zeus with an LND wallet which runs quite well on mobile phones using neutrino rather than a full Bitcoin node. Probably more common to use Zeus as a remote mobile UX to a full node running LND or CLN.

So, your lightning wallet choices are Phoenix or LND on mobile. Your privacy options using mobile lightning wallets are limited.

Running a TOR only full LND node from a PC is the only way to be truly private with lightning. There's a half dozen options for interfacing with it other than Zeus. BitBannana is also popular.

You can even use a miniPC which uses bugger all power.