The former L.A. Lakers star was found unconscious on Tuesday

By Adam Carlson and Elizabeth Leonard
Updated October 17, 2015 10:20 AM
Jason LaVeris/FilmMagic

Lamar Odom‘s medical improvement has everyone “in much better spirits,” a source close to the Kardashian family tells PEOPLE.

“The family is still totally consumed by what’s going on with Lamar, and Khloé is checking in with regular updates, but there was so much positivity [Friday],” says the source.

“The good news and Lamar’s improvement really lifted their spirits. They’re all just praying it continues.”

Odom, 35, was hospitalized Tuesday after being found unconscious in a Nevada brothel, with cocaine and opiates in his system and having suffered multiple strokes, a source confirmed to PEOPLE.

Family members rushed to be at his side, including most of the Kardashian family and Odom’s estranged wife Khloé Kardashian. Several of the Kardashian family members have since returned to Los Angeles, although it appears that Khloé remains in Las Vegas by Odom’s bedside.

Odom woke up Friday and was able to communicate with Khloé, a source previously told PEOPLE.

“The CAT scan came back clean, and they’re slowing taking him off each machine,” the source said. “He’s off dialysis and that looks good. We’re hopeful.”

Upon awaking, Khloé, 31, told him, “I love you,” the source said.

“He nodded, and that was the first response we got from him. That was so encouraging.”

“The good news and Lamar’s improvement really lifted their spirits,” the Kardashian source says. “They’re all just praying it continues.”

Several of Odom’s family members were spotted outside his Las Vegas hospital on Friday night, including his two children, Lamar Jr. and Destiny. Khloé’s friend Malika Haqq was also spotted arriving at the hospital on Friday.