The match disciplinary official, Murray Whyte from Ireland, has 36 hours from the final whistle to study the tape and bring any citings.
Lawes will discover by late Sunday night BST whether he has questions to answer over tackles on Argentina centre Gonzalo Tiesi and hooker Mario Ledesma.
Tiesi suffered suspected knee ligament damage when he was hit by Lawes after kicking the ball while Ledesma took a knee to the head.
Rugby World Cup regulations allow teams to refer incidents to the citing commissioner within the first 12 hours.
England’s assistant coach John Wells said they had not made any official complaints, despite flanker James Haskell appearing to accuse one of the Argentina players of eye-gouging.
“We have made no complaints about whatever happened then,” said assistant coach John Wells.
“There is a citing commission in place, and if they choose to do something as a result of what happened then so be it.”
Wells indicated England would not be using the referral facility during the tournament.
“As far as we are concerned, that structure is in place for others to use. Let them use it if they want to,” said Wells.
Haskell reacted angrily after a scuffle in the final seconds of the match and was heard via the referee’s microphone swearing at his alleged assailant.
ITV apologised for the language at the time and Haskell has subsequently followed that up with his own message of regret on Twitter.
“Just want to say sorry for the bad language, I clearly shouldn’t of [sic] sworn, bit of pressure out there. Onwards and Upwards,” he wrote.
Immediately after the match, Haskell played down the incident and said he just wants to move on.
“At the last breakdown I got a bit het up. I got cleared out, I had hands in my face and I think it was just a bit of over-exuberance in the end,” said Haskell.
“In the heat of the moment you react as you do. It is nothing really.
“It (eye-gouging) has happened to me a few times in my career. Tonight was nothing.
“I was obviously just stressed, it was a difficult game, we were under pressure. I got cleared out and had a hand on my face. It was nothing.”
England, who next play Georgia next weekend, arrived in Queenstown on Sunday, where they will train for the rest of the week.
The players will be given Monday off to enjoy some of local thrills but bungee-jumping is expected to be off-limits.