Trailing 4-0 and facing the prospect of the first Ashes series whitewash in 86 years, the England vice-captain was out in the 15th over after being dropped two overs earlier.
Strauss, who has scored only one half-century in nine innings in the series, needlessly chased a ball outside his off-stump and was caught behind by Adam Gilchrist for 29, leaving the tourists at 45 for one.
At lunch, England were 58 for one with Alastair Cook on 20 and Ian Bell not out seven.
It was the second ball of Lee's second spell after he replaced out-going paceman Glenn McGrath, who earlier had Strauss dropped in the slips.
Justin Langer had a poor start to his 105th and last Test match when he put down Strauss when he was on 21.
McGrath coaxed an edge which flew low to third slip, but Langer could not hold on to the two-handed chance and slumped to the ground in dismay.
But Australia didn't pay too dearly with Strauss only adding eight more runs before his dismissal.
McGrath, playing in his 124th and final Test at his home ground, bowled beautifully in his opening spell and beat the bat a half-dozen times as he got the ball to move off the pitch in the humid conditions.
Australian cricket is farewelling Test greats McGrath, Langer and Shane Warne, who have all announced their Test retirements.
McGrath and Warne, who have 1,263 Test wickets between them and have been the scourge of English batsmen for a good dozen years, have been match-winners in a golden era of Australian cricket, while the plucky Langer forms part of Australia's most prolific opening partnership with Matthew Hayden.
The Test got away 70 minutes late after morning rain and England's batsmen had to negotiate seaming conditions with the new ball.
England seamer Matthew Hoggard was ruled out of the Test with a side strain, and the tourists decided against playing an extra spinner with Jamie Dalrymple and went with paceman James Anderson to replace Hoggard.
Ricky Ponting's team has the chance to inflict the ignominy of a 5-0 series clean sweep, last achieved by Warwick Armstrong's 1920-21 Australians at home.