Undrafted rookie Trevor Daniel beat out Lechler in training camp. The two alternated punts throughout practices and preseason games. In Thursday's preseason finale against the Cowboys, Lechler averaged 42.4 yards per punt; Daniel averaged 40.8.
"Both guys had good preseasons," O'Brien said. "Shane Lechler, in my opinion, is a Hall of Fame punter. He's a guy that has meant a lot to us here and he really has competed at a high level, and Trevor's a good young punter."
Lechler, 42, said after the game that he felt this was the "first real" training camp competition he has faced since he has been in the league.
"I've had some competition before, but this kid is talented," Lechler said. "Very talented punter."
Texans star defensive end J.J. Watt praised Lechler as "truly the greatest punter of all time" in a tweet Friday.
The Texans also waived offensive lineman David Quessenberry, O'Brien said.
Quessenberry was diagnosed with cancer (non-Hodgkin T-lymphoblastic lymphoma) in 2014, just a year after he was drafted by the Texans in the sixth round. He made his NFL debut last December in a 34-6 loss to the Pittsburgh Steelers.
Lechler, who spent his first 13 seasons with the Oakland Raiders, said Thursday that he did not plan to retire if he did not make the team in Houston. If he signs with another team, the seven-time Pro Bowler will be entering his 19th NFL season.
The Texans signed Lechler to a one-year, $2 million contract in the offseason. Along with punting, Lechler was the Texans' holder. Daniel will likely assume those responsibilities.
"I've invested a lot of time," Lechler said. "If I was going to retire, I would have done it before the end of offseason workouts. I'm dug in. I'm going to play as long as I can. I still have something left in the tank."
ESPN's Adam Schefter contributed to this report.