According to the early spoilers for next week's episode, Danny has to tell Flack that his badge has been missing - which implies that he and Lindsay didn't tell anyone (although they could have told someone other than Flack, I suppose). Keeping it a secret is something Danny would do, but it's not something I would see Lindsay doing. Putting careers at risk - not to mention that their address is presumably on Danny's driver's license - it just seems to immensely stupid if time has passed between this episode and the next episode and they both kept the stolen badge secret. I expect stupid from Danny, but I would have thought Lindsay would avoid the same trap.
I could be wrong - we won't know until the episode airs. It's always possible that they changed something. But if the original spoilers for next week pan out, I'm curious to see just how they explain why the pair of them made such a boneheaded move.