"Well Virat's consistent. You've got to give him that, he's consistent," Lawson was quoted as saying by Fox Sports.
Kohli has been at forefront of the constant verbal battles in the ongoing series between the hosts and Australia.
"As a leader and as a captain of a cricket team where you've got lots of responsibilities, you've got to show more gravitas and responsibility than this. These sorts of actions are those of your worst behaved player," said Lawson.
"Send-offs are supposed to be against the code of conduct and he was certainly caught on camera using some bad language in the second Test match. I'm surprised he didn't get reported. But he must be treading a really fine line with the umpires and match referees because you're not supposed to give players send-offs.
"And his language has been pretty much unacceptable. And for a captain to then carry out a press conference and then just show so little diplomacy. But he's a great, great player. He's one of the best players going around, but you've got to behave as a captain better than that," Lawson added.