Lindsay Lohan's father on Wednesday claimed he was the mystery "friend" behind a planned appearance on David Letterman's TV talk show that involved the troubled actress.

Producers of "The Late Show with David Letterman" said on Wednesday that Lohan, 24, would not be appearing, as announced, because a mistake had been made. Initially, it seemed the talk show had been hoaxed by a prankster, but the actress' father Michael Lohan later claimed responsibility.

It would have been the first TV appearance by the "Mean Girls" actress since she was charged last week with stealing a $2,500 gold necklace, days after leaving her fifth stint in rehab in three years.

"We made a mistake. Someone purporting to be a friend of Lindsay's reached out to the show yesterday, allegedly on her behalf, and booked her to appear. Clearly, this person was not authorized to make commitments on her behalf," Tom Keaney, a spokesman for Letterman's production company, said in a statement.

By midday on Wednesday, Michael Lohan had told celebrity website TMZ.com that he made the Letterman booking after getting the green light from his daughter.

Michael Lohan, who recently repaired a strained relationship with his daughter, told TMZ that Lindsay "knew full well" about the booking. He said everything was going well until representatives for the actress got wind of the appearance and shut it down.

CBS announced on Tuesday that Lohan would appear by satellite to read Thursday's Top 10 comedy segment -- which has recently had fun with Lohan's numerous personal problems.

Lohan said in a Twitter message late on Tuesday that she was not doing the show and apologized for the confusion, adding "I'm not sure how this happened."

Lohan, once one of Hollywood's most promising young stars, is facing a possible three year sentence if convicted of walking out of a Los Angeles jewelry store in January without paying for the necklace.

She has pleaded not guilty to grand theft -- the most serious charge against her in three years of failed drug tests, missed court appearances and brief spells in jail stemming from a 2007 drunk driving and cocaine possession offense.