Lamar Odom: Security Guarding Hospital Room ... 24/7

Lamar Odom has a 'round the clock security team standing guard outside of his hospital room at Cedars-Sinai ... making sure the NBA star's privacy is protected at all times ... TMZ Sports has learned.

We're told the team wants to make sure Odom is comfortable and doesn't have to worry about anyone on the premises sneaking photos of Lamar in his hospital bed or sneaking out info of his medical records.

We're also told ... the hospital has limited the number of nurses, doctors and other medical staff who interact with Lamar ... because a smaller group of people means a smaller chance of a leak.