Lamar Odom Files Divorce Docs ...

Lamar Odom just filed his response to Khloe Kardashian's divorce petition ... and it shows the exes are lockstep when it comes to this breakup.

In the docs, obtained by TMZ Sports, Lamar lists the exact same date of separation as Khloe did -- December 13, 2013. Ditto for court's ability to award spousal support to the other. As we reported, our sources say they have a prenup.