My friend, I think the confusion stems from you thinking you have deep technical understanding on this, when everything you say demonstrates that you don't.

First off, you don't even know the terminology. A local LLM is one YOU run on YOUR machine.

Lumo apparently runs on Proton servers - where their email and docs all are as well. So I'm not sure what "Their AI is not local!" even means other than you don't know what LLMs do or what they actually are. Do you expect a 32B LLM that would use about a 32GB video card to all get downloaded and ran in a browser? Buddy....just...no.

Look, Proton can at any time MITM attack your email, or if you use them as a VPN, MITM VPN traffic if it feels like. Any VPN or secure email provider can actually do that. Mullvad can, Nord, take your pick. That's just a fact. Google's business model is to MITM attack your life, so we have the counterfactual already. So your threat model needs to include how much do you trust the entity handling your data not to do that, intentionally or letting others through negligence.

There is no such thing as e2ee LLMs. That's not how any of this works. Doing e2ee for the chats to get what you type into the LLM context window, letting the LLM process tokens the only way they can, getting you back your response, and getting it to not keep logs or data, is about as good as it gets for not having a local LLM - which, remember, means on YOUR machine. If that's unacceptable for you, then don't use it. But don't brandish your ignorance like you're some expert, and that everyone on earth needs to adhere to whatever "standards" you think up that seem ill-informed.

Also, clearly you aren't using Proton anyway because if you need to search the text of your emails, you have to process that locally, and you have to click through 2 separate warnings that tell you in all bold text "This breaks the e2ee! Are you REALLY sure you want to do this?" So your complaint about warnings is just a flag saying you don't actually know and are just guessing.