Vic says in there that Vaughn told her to hide the key. His clan went behind his back to sell it to the COV. At this point Vaughn is already friends (or at least on good terms) with Lilith and knows that she’s looking for the key. He wants to hide it from her too.
This isn’t me defending Vaughn’s characterization, by the way. I try to keep my criticisms fair but one thing I absolutely fully blame on the writers is the complete destruction of Vaughn as a character between Tales and BL3. The characters in Tales have so much depth, and instead they took one quirk and made it his entire personality. He went from nervous, nerdy accountant who happened to be super ripped under his clothes (funny!) to gym bro stereotype (annoying)!
Part of his character arc in Tales has him feeling like he’s becoming the dead weight of the group. In the bio dome, Rhys goes to hack the security turrets and has Sasha watching his back, and Fiona goes with Athena to collect the Gortys fragment. Vaughn is basically left to babysit an old man. But by the end of the story he’s stepped out of his friends shadows to become a leader, helping the survivors of the Helios crash to find their way on Pandora.
And then in Fight For Sanctuary all of those people are killed off screen and Vaughn just wants to be a bandit lord for no reason.
Anyway, I’m getting off topic. The point is that I think they were trying to go somewhere with Rhys and Vaughn being allies of the Crimson Raiders but being hesitant to help them open the Vaults. But as with so much of Borderlands 3, even if I’m right I’m still just annoyed that it’s another loose thread.