You can open the Lighthouse chest on characters that don't have a card and get loot.
Just completed my 7 streak on my Hunter. I already have the armor for them, so I decided to see what would happen if I swapped characters.
I went on my Warlock, saw that I could fly to the Lighthouse, opened the chest, KABOOM, so much loot and basically a full armor set. Actually insane that this worked.
If you really like the armor, but struggle with that class in pvp, do this.
Edit: I only opened the chest on my Warlock. As soon as I got 7 wins, I swapped characters and went.