Lawson was arrested Sunday morning after sheriff's deputies said he hit a parked car downtown and they saw him leaving the accident scene in the popular downtown Warehouse District. He posted $250 of his $2,500 bond on Sunday and was released from jail. No injuries were reported.
Browns coach Eric Mangini met with Lawson and said they had a "good conversation." Mangini did not say if Lawson apologized.
"I told him I was disappointed in him putting himself in that position," Mangini said. "The value in this and in any experience is what you can learn from it to make sure this type of thing doesn't happen again -- not just him, but anybody in our group."
Lawson was arraigned on Monday in Cleveland Municipal Court, where he pleaded not guilty to driving under the influence, physical control of a vehicle, hit-skip and not wearing a seatbelt. Court spokesman Ed Ferenc said Lawson's attorney asked for a jury trial.
He will appear in court again on Aug. 17. Lawson's car has been impounded, Ferenc said. The court did not have contact information for Lawson's attorney.
Lawson signed with the Browns as an undrafted free agent in 2008. He played in five games last season.
On Saturday, Lawson played in the team's scrimmage at Browns Stadium and returned two kickoffs.