When you use Tor, apart from the slower communication speed you will also consume more traffic which could be a small concern for those with a capped network. Each time you use Tor, apart from the Tor relay information you have to download, all your communication is also encrypted which adds an extra overhead.
It is possible to simply run the Lightning node on a VPS or other rented hardware and have that configured to connect to your Bitcoin RPC server running on your actual device, without the privacy disadvantages (as long as it's not running anything else) - but caveats listed here apply, since you want to prevent the transmission of passwords and stuff over HTTP.