Lindh, 26, was captured in Afghanistan in November 2001 by American forces sent to topple the Taliban after the Sept. 11 terrorist attacks. He was charged with conspiring to kill Americans and support terrorists, but pleaded guilty to lesser offenses, including carrying weapons against U.S. forces.
Lindh's lawyer and father said the lighter sentence given to should be reflected in Lindh's case.
"It is a question of proportionality. It is a question of fairness, and it is a question of the religious experience John Walker Lindh had," attorney James Brosnahan said. "And it was not in any way directed at the United States."
When Lindh was captured, he was videotaped being interrogated by CIA officer Mike Spann, reports CBS News correspondent John Blackstone. Soon after, Spann was killed in an uprising and an angry nation saw Lindh and Spann as opposites.
"The good American and bad American," Lindh's father, Frank Lindh, told Blackstone. "It was completely unfair. John was wounded and nearly killed in the same uprising where Mike Spann was killed."
Lindh converted to Islam and went to Afghanistan to fight for the Taliban against the Northern Alliance, which received U.S. backing.
On Saturday, Hicks pleaded guilty to supporting terrorism and acknowledged aiding al Qaeda during the U.S.-led invasion of Afghanistan. He was sentenced to nine months in prison. After spending five years at the U.S. naval base in Cuba, the 31-year-old former kangaroo skinner is likely to be transferred to a prison in Australia within weeks.
Brosnahan brokered Lindh's plea deal and said it was the best he could do in the political climate immediately after the 2001 attacks.
"In the atmosphere of the time, the best John could get was a plea bargain and a 20-year sentence," said Frank Lindh. "We love our son very much. He was wrongly accused when he was found in Afghanistan."
The White House referred telephone calls to the Justice Department, which declined to comment because it had not received Lindh's petition.