LINDSAY LOHAN was on 'The Late Show with David Letterman' and she told Dave she's finally hitting rehab on May 2nd.  Dave wasn't easy on her. He asked her straight up, 'Aren't you supposed to be in rehab now?'  And Lindsay replied, 'Don't you watch anything that goes on? What are you a tabloid now?'

He also asked her how long she'll be in rehab, and she said 'Three months.' He asked her how many times she's already been in rehab, and she said 'Several.'

Lindsay handled it fairly well, but it sounds like Dave caught her off guard because she said, 'We didn't discuss this in the pre-interview.'

She called her upcoming rehab stint, 'a blessing, not a curse.' Dave tried to get Lindsay to admit she's an addict, and to reveal what she's addicted to but she wouldn't bite. She told him, 'We've discussed this in the past.'  And he replied, 'Did we really? Now I'm the one who's having the blackouts.'

Meanwhile sources say Lindsay's rehab will take place in New York, and it apparently will be under lockdown conditions. She won't be given day passes, and if she leaves without permission, she goes straight to jail, no questions asked.

But before any of that happens, Lindsay is attending the Coachella music festival, which goes down this weekend and next.