Parece que eles se conheceram, mas tiveram um começo difícil. As coisas desceram de lá e as reuniões pararam muito rapidamente.
Sua próxima reunião não deu a James a oportunidade de melhorar as coisas com sua "cunhada" (James e Lily não eram casados) e seu marido.The first meeting between Lily, her boyfriend James Potter, and the engaged couple, went badly, and the relationship nose-dived from there. James was amused by Vernon, and made the mistake of showing it. Vernon tried to patronise James, asking what car he drove. James described his racing broom. Vernon supposed out loud that wizards had to live on unemployment benefit. James explained about Gringotts, and the fortune his parents had saved there, in solid gold. Vernon could not tell whether he was being made fun of or not, and grew angry. The evening ended with Vernon and Petunia storming out of the restaurant, while Lily burst into tears and James (a little ashamed of himself) promised to make things up with Vernon at the earliest opportunity.
Pottermore: Vernon & Petunia Dursley
This never happened. Petunia did not want Lily as a bridesmaid, because she was tired of being overshadowed; Lily was hurt. Vernon refused to speak to James at the reception, but described him, within James' earshot, as 'some kind of amateur magician'. Once married, Petunia grew ever more like Vernon. She loved their neat square house at number four, Privet Drive. She was secure, now, from objects that behaved strangely, from teapots that suddenly piped tunes as she passed, or long conversations about things she did not understand, with names like 'Quidditch' and 'Transfiguration'. She and Vernon chose not to attend Lily and James' wedding. The very last piece of correspondence she received from Lily and James was the announcement of Harry's birth, and after one contemptuous look, Petunia threw it in the bin.
ibid