The Proteas have suggested de Kock crossed the line after being subjected to personal barbs barked by Warner, while the tourists insist that is not true.
The first Test finished on Monday, but Australia's 118-run victory in Durban was marred by incredible leaked footage of Warner being restrained by teammates as he raged at de Kock. Other reports also alleged that Warner, himself, had made comments about De Kock's mother and sister and also called him a "bush pig".
The opening batsman celebrated aggressively after the South African was run out.
When asked if Warner's role as vice-captain was under threat, Lehmann said: "No, he's vice-captain of the Australian cricket team".
Sledging has got a lot of Australian cricketers in trouble over the years, with notorious incidents involving Pakistan's Javed Miandad, the West Indies' Curtly Ambrose and India's Harbhajan Singh.
"CA is working to establish the facts of what occurred and will not be commenting until this has been done".
The incident was discussed between the two team managers after play on Sunday night with match referee Jeff Crowe, who was on Monday still deciding whether to take action against players.
As De Villiers lay on the ground, Lyon, who had dismantled the stumps, dropped the ball on the South African, and left off to celebrate.
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"When he says something and someone comes back at him - then he gets upset".
Fronting the media after the conclusion of the Test, Smith said he wasn't aware of any sledging from his players that got personal, his counterpart Faf du Plessis claimed that both teams had committed the crime.
"I think there's always a line that you've got to be careful you don't cross".
At the time of the incident, Australia had taken control of the match and only needed one wicket on day five to take a 1-0 lead in the series.
Du Plessis said he was unsure about who started the incident, but was disappointed that the animosity between the two teams spread off the field as well.
He could also be fined 100 per cent of his match fee from the first Test.
Katich does not, however, understand or support the way Lyon responded to the de Villiers wicket.
'He executed a handsome run out. There was no malice in it, but it just didn't look good.
"There wasn't too much aggression", Paine said.
Australia fast bowler Mitchell Starc and South Africa batsman Theunis de Bruyn had a series of exchanges during one over, and Starc was apparently involved in a verbal altercation with some supporters near the boundary during the day's play.