The former NBA star, 36, has been transferred from the Los Angeles hospital where he's been convalescing to a specialised private facility.
The move comes almost three months after he was found unconscious and in critical condition at a Nevada brothel.
On Friday (8 January), a family spokeswoman confirmed that Lamar was released from the hospital earlier in the week.
Lamar's maternal aunt, JaNean Mercer, said: "Lamar continues to make remarkable strides and we are asking that you continue to respect our privacy.
"Again we thank all of you greatly, your support has been paramount in helping to uplift us during these past few difficult months."
The world was shocked when Khloe Kardashian's estranged husband was found unconscious at the Love Ranch brothel in Nevada in October where he is believed to have taken a drug overdose.
At the time, he was transferred from Las Vegas to Cedars-Sinai Medical Centre near Beverly Hills where he awoke from a coma after three days.
In November, Khloe confirmed he was no longer being kept alive on machines, but a series of strokes had resulted in brain damage.
On Wednesday (6 December), Khloe said: "[Lamar's] doing amazing and I'm so proud of the strength that he has to fight this battle.
"Because it's not my story to tell, I try to respect that, and I want him to be able to tell that story. I'm just there to support and care for him."
Some reports say it was Khloe who moved him in secret, avoiding any unwanted attention. Others say he has been moved close to Khloe's home in Calabasas.
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