Lamar Odom Breathing on His Own, 'Keeping Up With the Kardashians' Cameras Not Filming (UPDATE)

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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."

Lamar Odom's condition is continuing to show positive signs.

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.

WATCH: EXCLUSIVE: Ryder Cherry Leaves the Love Ranch Following Interviews About Lamar Odom

"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.

On Saturday, Kris Jenner, Kim Kardashian, Kendall Jenner and Khloe's best friend, Malika Haqq, took a private jet from Los Angeles and arrived in Las Vegas to reunite with Khloe, who hasn't left Lamar's bedside since arriving at the hospital on Tuesday night. Kim also postponed her baby shower scheduled for Saturday in the wake of Lamar's hospitalization.

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.

On Friday, ET learned that Lamar had opened his eyes and was able to communicate after being placed in a medically induced coma on Wednesday, following being found unconscious at the Love Ranch brothel in Crystal, Nevada, on Tuesday. According to Alvina Alston, a spokesperson for Lamar's aunt, JaNean Mercer, when his doctor asked how he was doing, Lamar gave a thumbs up and responded, "Good morning."

WATCH: Kardashians Return to Vegas to Visit Lamar Odom in Hospital

Here's more on Lamar's condition: