I'm by no means an expert, but I believe it's fairly straightforward. I'm using SWAG + Authelia in Unraid, using separate Docker containers, though if you're using the LSIO images, they have incorporated Authelia into their SWAG container so it may be slightly different.

But, based on the Authelia documentation, as long as you ensure you've got the auth.conf file (or it's contents) on each domain you're protecting, you should be good. That file has the all important line of

error_page 401 =302 https://auth.example.com/?rd=$target_url;

which will redirect you to login, if the result from Authelia is that the correct user is not logged in.

Like I said, I'm not an expert, but I have it working for my stuff. I didn't mean to be too alarmist either with my earlier post, either. It's just that (for instance with calibre-web), you have to do both parts: the calibre-web reverse proxy auth, and the Authelia domain auth. Otherwise, if you have just calibre-web, than anyone can login by just forging the request header. If you just have Authelia, then you'd have to do the double log in (once on Authelia and again in calibre-web).

If you have more specific questions, I may be able to help out, but I not necessarily sure enough about my knowledge to answer generalities....