Lee was charged with a level one offence by match referee Jeff Crowe for running down the wicket and celebrating what he thought was the wicket of England's Kevin Pietersen early on day two.
Umpire Steve Bucknor rejected the Australian appeal.
Lee faces being fined his match fee of 12,500 dollars (9,250 USD) if found guilty.
The International Cricket Council (ICC) is expected to announce the hearing's outcome at its Dubai headquarters later Sunday.
Lee's report is the latest to have blighted Australia's on-field disciplinary record over the past 18 months.
Captain Ricky Ponting was fined 75 percent of his match fee for dissent when he was run out by England substitute fielder Gary Pratt at Trent Bridge last year.
Batsman Simon Katich was docked half his match fee for showing dissent towards an umpire's decision in the same match.
Lee, paceman Glenn McGrath and wicketkeeper Adam Gilchrist were all penalised for incidents last summer, for showing dissent and using obscene language, while Shane Warne was cleared of a charge of dissent.
Ponting has also tested the patience of match referees in 2006.
He was fined 25 percent of his match fee for showing dissent towards an umpire's decision in a Test against Bangladesh in Chittagong, and was docked his entire match fee for dissent during a day-night match against the West Indies in Kuala Lumpur.