Amanda and Lydia became enemies from the day they met, Lydia helped frame David and Amanda turned Victoria against Lydia. Amanda managed to kick her out of the Hamptons but she returned asking for revenge twice. The second time she exposed her to Victoria which led to the shooting in Amanda's wedding.
In "Pilot", Emily and Lydia met at the beach just after Emily had rent the house. Later that day they met again when Conrad suffered an attack and Emily pretended to unknown that he wasn't her husband. Then at the Memorial Day Party Emily told Victoria that she and Lydia met at the South Fork Inn revealing that she had an affair with Conrad