Lamar Odom did indeed tweet his support of the Kardashian family earlier this week -- contrary to what his friends are saying.
An angry tweet -- purportedly from Lamar -- went out a few days ago, in response to his father claiming the Kardashians are the reason he's fallen into a deep, dark hole.
The tweet trashes his dad, and then praises the Kardashians -- "He disrespecting the ONLY FAMILY that has loved me without expecting anything in return," adding, "They are the ONLY ones that have been here consistently 4 me during this dark time."
A source close to the Kardashian family tells TMZ ... just before pressing the button, Lamar called the family, saying he was about to tweet the message.
And we're told ... when Lamar called he was on speaker, so Khloe, Kim, Kourtney, Kris and others heard Lamar say he was tweeting his message.