Lamar Odom Will Survive with Months of Rehab, Khloe Will Be By His Side

Lamar Odom will survive his near death experience but it will be a long, hard road, doctors say ... and we've learned Khloe will be with him the entire way.

Doctors are telling Lamar's friends and family rehabilitation will take many months, and they believe an undetermined amount of damage to his body will be permanent.

We're told Lamar will have physical, speech, and other therapists working with him for the foreseeable future.

As for Khloe, our sources say she has vowed to stay with him through the entire ordeal ... and that includes all therapy.

She has kept a constant vigil by his bedside so far and she is determined to see this through.

TMZ broke the story, Khloe and Lamar have both signed final divorce docs, but the papers will not be signed by a judge for 2-4 months.

We're told Khloe has said nothing about her intentions with Lamar, or how her decisions might impact her relationship with James Harden.

One thing we do know ... Khloe dragged her feet for more than a year after filing for divorce, because she still loved Lamar and wanted to save him.