Rescuers found the toddler Saturday hanging upside down in the car, which had crashed into a frigid Utah river a day before.
Lily's mother, Lynn Jennifer Groesbeck, died in the crash that had landed their car on its roof in the Spanish Fork River. She was 25.
Deven Trafny, 34, was out of town on a job at the time of the accident, CNN affiliate KUTV
reported. He rushed to his daughter's side as soon as he heard.
"(I) came in, I put my finger in her hand, and I told her her Dad was here, and I love her," he told reporters Wednesday. "I haven't left her bedside since, and I've just been here just sitting next to her waiting for her to get better so she can come home."
Trafny said that Lily is awake and has been singing nursery rhymes. Video of the two of them at a hospital shows her waving at a camera.
"She knows everything she knew before anything happened. It's amazing. Doctors say it's amazing," he said.
Lily might have died unseen with her mother had a man not gone fishing in that particular spot Saturday. The angler waded into the river around noon, then noticed the car wheels-up in the water. The fisherman called emergency dispatch.
The water was so cold that, when the rescue was over, seven of the men involved had to be treated for hypothermia.
They heaved the car onto its side and saw Groesbeck in the driver's seat. It was clear to them that she was dead.
Lily was still strapped into her seat, where she may have been for 14 hours, if the wreck occurred at about 10:30 Friday night, as police believe.
Trafny described Groesbeck as the love of his life, according to KUTV: "I'm going to miss her a lot. I still have to deal with that."
But he also considers himself lucky to still have his daughter -- healthy and alive.
"I'm just blessed. I'm counting all my blessings right now," said Trafny.