David Letterman let loose last night on Lindsay Lohan, asking her, "Aren't you supposed to be in rehab?" And he prodded: "How many times have you been to rehab? ... What are they rehabbing, first of all? ... Why are you always in trouble?"

Lindsay quipped back, "We didn't discuss this in the pre-interview." She went on to tell Dave, "I'm happiest when I'm working and the healthiest and I think this is an opportunity for me to, you know, focus on what I love in life. I don't think it's a bad thing. I think it's a blessing and not a curse."

The interview wrapped with Lindsay practically in tears ... she called Dave "very sweet" after he complimented her for having "enough spine, enough sense of yourself, enough poise to come out here and talk to me."

Lindsay told the audience she's actually "looking forward to rehab," saying, "I'm looking forward to some time for myself. The next time I come on the show, that will be in my past."

When we snapped her on the way in she was in relatively good spirits, but on the way out she couldn't resist working it for photographers in this short 'n sexy leather skirt ... hawt!

Lilo tweeted, "Had a wonderful time at the @Late_Show. It was great fun! #iHeartDave."

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