Sarah Murnaghan had the procedure at Children's Hospital of Philadelphia.
In a post on Facebook her mother, Janet, said Sarah was now out of surgery and said her doctors told her it "went well."
Later Tuesday evening, Janet posted more:
"Sarah is still mostly sedated, waking periodically in pain, so aggressive pain management is underway. She has one chest tube back in place.
"Tomorrow we will start slowly weening vent settings. By next week I expect we will know whether her other muscles are strong enough to do the job of breathing after extubation or if she needs a temporary tracheostomy while we recondition her muscles. Praying she can do this without a trach.
"So proud of her strength and determination. This is her fourth surgery since June 12 (1st tx, ECMO, 2nd tx and diaphragm plication). Sarah and her two donors are my heros!"
Sarah was back on a ventilator because of partial paralysis of her diaphragm, a common complication of transplant surgery.
The family revealed Friday that Sarah received a second set of lungs after the first failed within hours of a June 12 transplant.
Sarah had end-stage cystic fibrosis.
The suburban Philadelphia girl initially received lungs from an adult donor after her parents sued over national rules that place children behind adolescents and adults on the priority list for adult lungs - even if the children are sicker and are capable of accepting adult organs.
The Murnaghans and the family of 11-year-old Javier Acosta of New York City challenged the policy making children under 12 wait for pediatric lungs to become available or be offered adult lungs only after adolescents and adults on the waiting list had been considered. Both children have end-stage cystic fibrosis.
A federal judge ruled they should be eligible for adult lungs after U.S. Health and Human Services Secretary Kathleen Sebelius declined to intervene.