Can you trade the Nintendo DS Lite for the Nintendo DSi?

If you mean simply trading one system for the other, then no, you cannot. The Nintendo DSi is worth about $150 while the DS Lite is worth about $110.

You can, however, trade in the Nintendo DS Lite and cash for the Nintendo DSi. If you choose that method, you will need about $40 or so more to cover the cost. You can also choose to trade in your Nintendo DS Lite plus a game or two for the Nintendo DSi.