Lee, who was traded to the Browns last week after 11 seasons with the San Francisco 49ers, will wear No. 8 in Cleveland as a tribute to his daughter Madelyn, who lived just eight days in January before she died from complications after her birth.
"I think sometimes, not necessarily by me and my wife, her life can get overlooked. She was here, she was a person but nobody got to meet her, nobody got to see her," Lee said, according to the team's website. "She was really alive and really a person. It's a way to honor her and kind of just give her some glory she deserves."
Madelyn was Lee's third child with his wife, Rachel.
"It's been life-changing, some good ways, some bad ways. It's made me appreciate the two boys that I do have, my wife, my family," Lee said Thursday.
"It shows how fragile life is. It's also changed the way I feel about dying. I don't want to die, I don't want to leave my wife and kids. But also, I get to see my little girl some day."
Lee wore No. 4 with the 49ers. He is a three-time All-Pro and the 49ers' franchise leader in punts (941), punting average (46.2 yards), net average (39.5 yards) and punts inside the 20-yard line (300).
ESPN.com Browns reporter Pat McManamon contributed to this report.