The 35-year-old basketball star had the strokes - which are believed to have impacted his motor skills - soon after his collapse, but doctors have only just discovered them following a series of brain scans.
TMZ reports that they have affected Lamar's ability to walk and talk and Lamar is also believed to be suffering from "major kidney failure".
It has been claimed that he may need to undergo a kidney transplant.
A source has claimed the athlete's organs are all functioning at various levels again, but "his kidneys are shot".
The insider told the site that Lamar, who is said to be suffering from aspiration pneumonia, is set to have six hours of dialysis - a process to remove waste and excess water from the blood and is used primarily as an artificial replacement for lost kidney function - a day, but could eventually need a kidney transplant.
Doctors in Los Angeles are also planning to perform more tests on his brain in a bid to establish the full extent of the damage from the strokes.
However, the former Khloé & Lamar star's aunt JaNean Mercer insists he's making "miraculous progress" and "taking a few steps."
In a statement, she told PEOPLE.com: "As Lamar begins a new chapter in his road to recovery, PLEASE continue to uplift him and the family in prayer. He continues to make miraculous progress, taking a few steps in Los Angeles. We couldn't be more overjoyed!"
- Bang! Showbiz
