Lee said his bowling action was also "questioned" at the start of his career and he could relate to Murali's feelings.
"I went through the same procedure at the start of my career. I was not accused (of chucking) but my action was questioned -- it was not up to the scratch.
"I had to appear before a ten-member panel and it was great when the results came and my action was okayed," the 27-year-old Aussie bowler said at a press conference in New Delhi.
"I think we should let Murali carry on with his game. Not only Murali but Shoaib as well. Shoaib is a wonderful cricketer and a great friend," said Lee, the brand ambassador of Timex. He was in New Delhi to launch the company's 150 years of watch collection.
"I think media focusses more on bad things. I think media should concentrate on good things like the recent India-Pakistan series when the two countries came really close," said Lee.
Murali, who is just seven short of overtaking the world record of highest Test wickets, has been dogged by the chucking controversy and a report on his 'doosra', the ball that moves away from the right-handers, is being studied by the International Cricket Council (ICC).
Asked to comment on the infamous Aussie sledging, Lee played the straight bat and said "Aussies play their game hard. We do not acknowledge sledging. We call it gamesmanship, friendly banter.
"There is nothing wrong in chatting with a batsman. But we don't step the line because we know what the consequences can be and the action. We play our cricket very fair," said Lee who has taken 139 wickets in 37 Tests at an avearge of 31.66.
Looking forward to Australia's upcoming cricket tour of India in October, he said, "It will be a challenge. It will be very tough but also enjoyable and some very good cricket will be on offer. I had a chat with Sourav Ganguly -- he is a close friend -- he is very fired up and excited... May the best team win."
The tearaway speedster conceded that India-Australia rivalry had the potential to overtake that of the Ashes.
"We grow up thinking about Ashes being the most important. We share a love-hate relationship with them. We love winning and hate losing to them. Now I think such a relationship is building with India as well. It is great watching Tendulkar, Dravid and Laxman bat. It is fantastic."
Lee, who would be coming to India for his first Test tour, said he had not set any personal goals for himself but would certainly look to make it memorable.
"I will try and have a very good tour. I know the conditions in India do not suit fast bowlers but Kapil Dev has done well. I will try to emulate him."