Instigator Williams lost his head during the scrap as was seen swinging his arms in an aggressive manner towards Lyon midfielder Lucas Tousart.
Williams was very fortunate to escape with just a yellow card from referee Bas Nijhuis and will almost certainly face retrospective disciplinary action when UEFA review the footage.
But Williams played down the incident when quizzed by BT Sport after the final whistle.
He said: 'It's what happens, it's football. It is what it is. It's just what happens, it's football and stuff happens. It was one of them things I suppose.'
Lopes later retorted: 'I don't think it's part of the English atmosphere to hit an away player but it was like that.'
Lyon forward Bertrand Traore was shown a yellow card after confronting the fan who struck his team-mate.
Traore told L'Equipe: 'In these heated moments, like the fight, we have to help each other, stay as a team. That's what I tried to do. There's a supporter who puts a blow to Anthony Lopes, I think it's not normal. I defended him.'
The incident occurred midway through the second half when the score was 1-0 to the visitors.
Williams later equalised for Everton, only for Traore to restore the Lyon lead which had earlier been established by Nabil Fekir.