Lawrence, upgraded from critical a day earlier, was expected to remain the same for the next few days, said Kris Carraway-Bowman, spokeswoman for Los Robles Regional Medical Center.
"He's definitely not out of the woods by any means, but this was a man who was near death who has made a miraculous comeback," she said.
The former star of TV's Martin sitcom was alert, focusing his eyes and able to follow doctors' commands. He remained on a ventilator.
Lawrence, 34, was trying to lose weight for a movie role when he went for a jog Sunday near his Westlake Village home in 100-degree weather. His girlfriend found him collapsed on the doorstep an hour later and called 911.
Lawrence's temperature had risen to more than 107 degrees when he reached the hospital. Doctors said he suffered acute hyperthermia.
Lawrence has faced both health and legal problems in the past.
In September 1997, he was sentenced to two years' probation and community service for his part in a nightclub scuffle. The actor, who pleaded no contest to battery, also was ordered to remain in a treatment program.
A statement from Lawrence's publicist at the time said the actor was in a "medically approved" program that was not for treating a substance abuse problem.
In May 1996, Lawrence was detained by police and hospitalized after he was found yelling and screaming in the middle of a busy Los Angeles intersection. He had a gun in his possession.
Lawrence had failed to take prescribed medication and had suffered a seizure, his physician told police.
Two months later, he was arrested at Burbank Airport after police found a loaded handgun in a suitcase he was taking on a flight to Phoenix.
Martin debuted in 1992 and was canceled by the Fox network in November 1996. His film credits include Life, Bad Boys and Nothing to Lose.
He reportedly is scheduled to star in an upcoming Warner Bros. comedy, See Spot Run, playing a postal worker who adopts a special dog.