In theory a LN node on only a tor hidden service giving invoices over a hidden service would be private. Especially if payments are routed with AMP. It's just the lead time of these new features being widely available on peers to be able to do it yet. It needs more infrastructure support before it could be trusted and some sims to attempt to unmask the endpoint's IP address to ensure there isn't any leak.

Mainly it's just someone tailoring a deployment to this use case, perhaps writing a controller that automates it for you and enough people making these hidden endpoints to hide among. So it will take time to happen.