This time around, the vault dweller is named Lucy (Yellowjackets’ Ella Purnell), and she experiences a lot of the series’ key moments in the short trailer. That means horribly mutated animals, slapped-together cities, the militant Brotherhood of Steel, vault uprisings, some Wild West shootouts, and a very good dog who is also a killer. And of course, there are the classic tunes — in this case, it’s Nat King Cole’s “I Don’t Want To See Tomorrow.” The show is set 200 years…