Yes you can run this from a flashcard. I'm not saying it will run out of the box on your R4 flashcard. We had someone yesterday who had to put another kernel on his R4 for it to run. Best place to start is to just
put both latest GBARunner2 for DS named 'GBARunner2_
arm7dldi_ds.nds' and 'GBARunner2_
arm9dldi_ds.nds' on your sdcard together and see if they run your ROMs. If they do you're good. Also the compatibility is around 70% for running it from a flash card as you can see from this slightly out of date
compatibility list.
Obviously in your case using a DS Lite the best way to run your GBA ROMs would be with a slot2 flashcart at the moment.