Lynch has made steady progress at the U.S. military hospital in Germany where she has been treated, officials said Friday.
Lynch, a 19-year-old from Palestine, W. Va., left Ramstein Air Base, along with members of her family, early Saturday.
Lynch was captured March 23 after her 507th Maintenance Company convoy was ambushed in the southern Iraqi city of Nasariyah. She was rescued from a hospital in the city April 1 by U.S. commandos and airlifted to the Landstuhl Regional Medical Center in western Germany.
Lynch is being treated for a head wound, an injury to her spine and fractures to her right arm, both legs, and her right foot and ankle. Gunshots may have caused open fractures on her upper right arm and lower left leg, according to the hospital.
It remains unclear whether the injuries were received when her unit was ambushed or while in captivity.
Hospital spokeswoman Marie Shaw said Friday that Lynch's condition is continuing to improve.
"She slept well and is in good spirits, and had blueberry muffins, cereal, a strawberry milkshake and apple juice for breakfast," Shaw said.
Although she cannot yet stand, Lynch has been able to sit up and talk with her parents, sister and brother and a cousin, who have been staying with her at the hospital since Sunday.
CBS News Correspondent Bill Whitaker reports her family says they don't want the media glare to interfere with Lynch's recovery. Doctors say that though she will require more hospital treatment and physical therapy, they do expect her to make a complete recovery.
Lynch's father, who arrived Sunday from West Virginia along with her mother, two siblings and a cousin, said the family was happy to discover that her condition was not as bad as they had feared.
"It really felt good once we'd seen her and seen the spirits she's been in," Gregory Lynch told reporters during the family's first news conference at Landstuhl. "We knew she was going to be all right."
Deadra Lynch said her daughter was "real cheerful," emphasizing that the family was not pushing her to discuss her harrowing experience in Iraq.
"When she's ready to tell us something, she will," said her father.
Lynch does know that some of her colleagues lost their lives in the ambush that led to her capture and that others risked their lives to save her, reports Whitaker. It's unclear whether she had asked about their fate after being rescued or already knew about it.
Seven other American troops are listed as prisoners of war and 11 are considered missing in action. Twenty-three Americans were taken prisoner in the first Gulf war.