UPDATE: Despite a report that Lamar Odom was helped out of his hospital bed and was assisted in moving to a chair, a source close to the family tells ET that the 35-year-old athlete did not leave his hospital bed, but did get up. However, he's "still very weak."
The former NBA star is now breathing on his own and is "alert and stable," a source tells ET. We're also being told that Lamar is completely off a ventilator.
Despite the improvements, Khloe Kardashian's ex is still in the Intensive Care Unit at Sunrise Hospital in Las Vegas, Nevada, and is considered to be in critical condition. On Sunday, he received dialysis treatment after previously experiencing kidney failure.
"He is showing improvement in his condition, however, regaining complete organ function continues to be a top medical priority," a source says.
Contrary to some reports, Keeping Up With the Kardashians is not currently filming during Lamar's medical crisis. The reality show was set to resume filming at the end of October, but now, it may be delayed.
"Reports that the show is filming are inaccurate and hurtful to the family," the source adds.
Khloe's older sister revealed on Saturday that she and Kendall were even able to make Lamar smile.
"I have faith in you," Kim Instagrammed alongside a flashback photo of her and Lamar dancing together at a black tie event. "I believe in the power of prayer and positive energy! Thank you all for your prayers! Lammy- I'm so happy Kendall and I could make you smile today! God is good!"
A source tells ET that in addition to Khloe, Lamar's father, Joe, and his two children, Destiny and Lamar Odom, Jr., have been with the former Los Angeles Lakers player the most during his hospitalization. In particular, Khloe, who's still legally married to Lamar, has "been by his side constantly," another source confirms.