David Letterman GRILLS Lindsay Lohan -- Are You An Addict???

David Letterman grilled Lindsay Lohan like a cheeseburger today ... firing off question after question about her upcoming stint in rehab ... until Lindsay finally shot back with a dig of her own.

Letterman broke the ice by asking, "Aren't you supposed to be in rehab now?"

Lindsay responded, "Don't you watch anything that goes on? What are you a tabloid now?"

Lohan eventually told Dave what he wanted to hear -- she'll be entering rehab on May 2 and believes it's "a blessing and not a curse."