#Excellent combo.

You quoted all the relevant rules. To read lips, you need to

> see a creature's mouth while it is speaking a language you understand

And with the Eagle totem at 6th level, you get to clearly see creatures and fine details (like moving lips) within 1 mile. It is legal and a great idea.

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Regarding realism, as pointed out in the comments, it's not very easy (or [possible][1]?) to read a human's lips at 100 feet away. Depending on the size of what you are observing (like anything smaller than a Giant creature), the DM can certainly rule that you can't read its lips. That being said, the Observant feat doesn't require anything other than being able to see a creature's mouth, and the Eagle's Eye lets you see fine detail (do moving lips count?), so at least by RaW it should work. It depends on your table and how realistic or rules-adherent you are.

*I would allow it as a DM*, I think it's an awesome idea and it's something that isn't seen very often. Heh, the Barbarian is actually a ranged sniper/scout guy?


  [1]: https://www.jstor.org/stable/44387941?seq=1#page_scan_tab_contents