The 26-year-old left-hander had been hospitalized in Santo Domingo since the accident on Nov. 24.
His condition is now stable enough to allow the team to move him, team spokesman Bart Swain said.
"It's definitely a step in the right direction for Juan," he said.
Lara suffered a fractured spine, severe brain trauma, two broken ribs and a punctured lung in the crash.
Lara, a Dominican native who pitched in one game for Cleveland last season, was returning from a Winter League game in San Pedro de Macoris when the sports utility vehicle he was driving was hit by a motorcycle. The accident killed the motorcycle's driver and passenger.
Lara was stopped at an intersection when his vehicle was struck on the driver's side.