Lindsay Lohan -- I Respect DAVID LETTERMAN More Than Court

There's one person in Lindsay Lohan's life who she wouldn't DARE to cross ... David Letterman ... and the actress made sure to get her ass to his studio on time today so she could appear on his show tonight.

Lohan is supposed to talk with Dave about "Scary Movie 5" -- but it's likely Letterman will ask about her personal life ... maybe even why she blew off a deposition in Los Angeles this week.

We broke the story ... Lindsay was supposed to be deposed as part of a lawsuit filed by a paparazzo who claims Lindsay's assistant hit him with her car and put him in the hospital.

Fun Fact -- the Letterman chat will be Lindsay's first TV interview since Nov. 2012 when she appeared on "The Tonight Show."