The 35-year-old basketball player was admitted to hospital
on Ocotber 14 after being found unconscious in Dennis Hoff's Love Ranch South, reported E! Online.
He has not regained consciousness and remains in a "critical" condition.
The incident has left the "Keeping Up With the Kardashians" star feeling "completely inconsolable and heartbroken".
The Kardashian family, however, has not been surprised by the news.
"(It) isn't shocking, but it is sad," said the source.
Khloe and Lamar wed in September 2009, exactly one month after meeting at a party, but filed for divorce in December 2013, with the agreement being finalised in July this year.