Hookes, a former Australian cricketer, died after being punched outside a bar in Melbourne three years ago.
Restoking his criticism of Australia's "ugly" on-field behaviour, Gavaskar said that someone might "whack" the cricketers if they spoke and acted in a bar similarly to how they behaved on the field.
"There's the example of the late David Hookes," Gavaskar said on the sports network ESPN.
"Would the Australians, who use that kind of language on the field, and not all of them do, (use it) in a bar and would they get away with it?
"Some day, some other hot-head guy might actually get down and, you know, whack somebody who abuses him."
The reference to Hookes incensed Border and Lehmann.
Border, who has been friends with Gavaskar for 20 years, was particularly upset.
"I consider Sunny a friend, but what he said about David Hookes and the behaviour of Australian cricketers was totally uncalled for," he told The Australian newspaper Thursday.
"What Sunny said on television was totally inappropriate. For him (Gavaskar) to link David's death to players allegedly misbehaving on a cricket field is plain wrong," Border said.
Lehmann said Gavaskar's remarks about Hookes were "out of order."
"I'm pretty disappointed with Gavaskar. His remarks only hurt David Hookes' family and friends and tarnish Hookesy's memory," Lehmann told the newspaper. "A man of Gavaskar's stature in the game of cricket should know better.
"His outburst about David Hookes was totally out of order and in bad taste.
"As to what he said about the way Australia goes about playing the game, he's overlooked the fact there are officials who are empowered to take action if someone is out of order."
"I came into the international arena a few years after he had retired. He was a player I admired -- not any more," Lehmann added.
Border said Gavaskar has a mistaken cultural belief in the way Australia play their cricket.
"Where Australia may be seen to be playing the game hard and tough could be misconstrued on the sub-continent," Border said.
"Similarly, the way India plays the game at times may not be to the liking of every Australian. Cricket is a global sport in which different cultures lock horns out in the middle, only the nuances of the game may vary from country to country.
"While a cricketer on the sub-continent or the West Indies may find an Australian bowler's remark to a particular batsman of 'you lucky bastard' offensive, to players in other teams it's not.
"Sunny has missed the point here badly. He's clearly overlooked the fact there are different cultures at work.
"I think he is drawing a long bow blaming our cricketers for misbehaving. While I do admit words are said out in the middle, we play the game hard, but fair."
The Melbourne Age said Gavaskar's reference to Hookes' death was "clumsy. At worst it was offensive."
Cricket Australia said it was disappointed with Gavaskar's comments, given the former batsman's status with the International Cricket Council, where he is the chairman of the governing body's cricket committee, but would not dignify them with a response.