Leaked footage of the acrimonious blow-up, which had unfolded at tea on day four of the first Test in Durban, shows Warner being restrained by teammates and it has ignited another war of words between the rivals.
Former South African spinner Paul Harris went as far as saying Warner has "all the characteristics of a bully".
Steve Smith says Warner reacted to personal sledging from de Kock that had crossed the line. Australia's captain refused to confirm what was said, but it's understood it involved Warner's wife Candice.
Read more: What Australian cricketer David Warner really said in ugly tunnel incident with Quinton de Kock
South African skipper Faf du Plessis insists both sides were guilty of barking personal verbals on the field, a claim disputed by Smith.
Australia's coach was reluctant to add fuel to the fire, but made it clear the saga hadn't affected Warner's standing as a leader.
Read more: Family members bite back at Warner
"We're certainly supporting David. We want to play a way that gets us success and we've just got to make sure we don't cross the line - that's the key," Lehmann said.
"There are things that cross the line and evokes emotion and you've got to deal with that behind closed doors and get better at that."
Both sides are going to push the boundaries. That's part and parcel of Test match cricket. It's a bloody tough game.
"This series is going to be played very hard on the field by both sides, it looks like ... the way they want to play is fiercely competitive on the ground. As long as it doesn't get personal, that's probably the key."
Lehmann floated the prospect of Smith and du Plessis smoking the peace pipe at some point before the second Test starts on Friday in Port Elizabeth.
Crowe has already reminded both camps of the need to play within the spirit of the game and it wouldn't be a surprise if he does the same before day one at St George's Park.
"I'm sure the captains will chat and the coaches will chat and we'll get away to play the game," Lehmann said.
"The cricket is the most important thing."
Crowe has already finalised a punishment for one misbehaving Australian in Durban, fining Nathan Lyon 15 per cent of his match fee for his 'ball drop' send-off of AB de Villiers.
"It was probably a bit cheeky. The great thing about it, he apologised to AB straight away. He sent him a text, spoke to him today and it's dealt with," Lehmann said.
"That's how it should be as grown men."
- AAP