Michael Lohan -- I Booked Lindsay on Letterman

In case you haven't heard -- Letterman had to issue a retraction this morning, explaining Lindsay would not be doing the "Top 10" bit on Thursday as they had announced yesterday -- after Lindsay tweeted that she NEVER agreed to do the show.
Letterman's people released a statement explaining how someone "purporting to be a friend of Lindsays" reached out to them and made the booking ... but Dave's camp didn't reveal the name of the friend.
But Michael says he was behind it -- telling TMZ he got the idea after Dave cracked a joke at Lindsay's expense during Friday's "Top 10" ... and Lindsay was into it.
Michael says Lindsay "knew full well" about the booking ... they even discussed transportation from the L.A. studio, where Lindsay would be doing the bit via satellite.
Michael insists everything was going smoothly -- until Lindsay's reps got wind of the appearance and shut it down.