The DSi is going to have a download store, so some older games may show up there.
This is the only official word (or, indeed, any word at all) I could find about the future availability of the DS Lite. An interview with NoA's executive VP of sales and marketing. It's pretty noncommittal, but suggests they won't be discontinuing the DS Lite when the DSi launches. At least, not right away.
Even if they do discontinue it, I'm sure you could find one second hand, if you wanted one. Wired, October 3, 2008: Wired.com:
The Nintendo DS Lite. I think the big question is: Is the DSi a product that’s going to sit on shelves next to the DS Lite, or is it a replacement for the DS Lite? Dunaway:
Right now we’re still working through what the strategy's going to be here. But we think that there's huge untapped potential for the DS Lite. Because when you’ve got only one in every five households in the U.S., compared to one in every two in Japan, it says there's potential.
You’ve seen some of the work we’ve done this year with celebrities, that we're bringing a lot of new consumers in to the DS. So I think there’s opportunity for both of them to coexist for some period of time.