How did she work out that Bobby had killed Lucy?

I told her.

Peter told her at Lucy's grave in there last episode, we didn't hear the confession as the scene was filmed a while before Jacqueline Jossa went off on her maternity leave but Lauren knows so if they are charging Max expect Lauren back very soon.

How do we know that Peter told her? Could it be a red herring?

I can't remember but what did she find that made her think it was Jane?

There was a scene ages ago where Lauren told Jane that she (Lauren) had gone to see Lucy, got as far as the front door, then turned back (part of the footage of Fatboy's phone showed some of this). Jane backed her up, as she was inside watching, but her statement to the police said that she had been in Masood's house all evening/night, so Lauren guessed that she had lied about her alibi.

Lauren found Emma's file on Lucy .
Lauren got a wedding card for Ian and Jane, in which she wrote "I know what happened to Lucy. She died at home."