Yes, you can use ds lite games in the original Nintendo ds. They are not making new specialized games for the Nintendo ds lite. they are still making games that fit both the original DS and the Nintendo DS Lite.
Nintendo offers a "Nintendo Ds Lite 5 in 1 Combo Nintendo Lite Ds Case" for your Nintendo DS. The case can hold the Nintendo DS console, and has a compartment inside that you can put NDS cartridges, GBA SP cartridges, and stylus etc.