The 'investigation' in the pub was somewhat silly.
Why is Lydia bothered about who killed Craig ?
Why are any of them bothered? If one of them confesses will they make a citizen's arrest and take them off to Hotton Police Station?
Of course not !!! It would just mean there are loads of people needing to keep a secret.
Lydia knows that Ceaig was guilty. Why does she need him to admit it to her.