Nintendo president Satoru Iwata, in one of his many post-GDC interviews, expressed his hope to see the Nintendo DS shortage ending soon.
"I'm hopeful in the latter half of April we can get rid of the terrible, terrible shortage situation that we are facing with the Nintendo DS right now." Iwata characterized current demand as "unpredictable".
Not being able to sate demand for nearly a month suggests that the DS lite may indeed take awhile to arrive on shores outside Japan. We'll just have to see what develops.