Odom Custody Case: Lamar Odom Fighting Baby Mama in Custody Case

Lamar Odom is in a New York courthouse right now ... battling it out with baby mama Liza Morales over child support and visitation ... and it must be exhausting because Lamar fell asleep on a bench in the hallway.

Lamar told TMZ ... he was exhausted with jet lag, which is why he fell into a deep sleep before the hearing. Cops actually became concerned because the Clippers star wasn't moving, so they nudged him awake.

On Liza's way out of court, we asked her if she happened to see Lamar snoozing ... and she laughed, saying, "He's tired."

In addition to child support and visitation, they're reportedly bickering over whether their son and daughter can appear on their reality TV shows. Lamar is on "Keeping Up with the Kardashians." Liza was on a show called "Starter Wives."

And get this ... we asked Lamar about being in the same restaurant last night as Kris Humphries. As we reported, they didn't speak ... but Lamar told us he didn't see Kris and would have gone up to him and said, "What's up," if he knew.

Bros before ...