You can do a lot of things with a DS Lite, of course depending on your flashcard and if you add a memory expansion pack, you can do more.
First of all, it is necessary to know if your flashcard is SDHC or not, in which case you will have to prepare one or more micro SD cards according to your wishes of course.
From what I understand you are starting from a configuration of an R4 without memory expansion pack, we can therefore exclude the possibilities that a DSTwo would have offered you, but it doesn't matter already just with a simple R4 you can do a lot.
Last year, I had fun making a little pdf illustrating the possibilities of a DS Lite with an R4 combined with a memory expansion pack, I'll leave this as an attachment.
Without a memory expansion pack, it doesn't change much, you will still be able to get most things working.
Since this pdf, my configuration has evolved, we can add to everything that is already mentioned, Fake-8 (pico-8), UNXDS (UNX VM), MegaZeux (DOS games), GZOIS (Sharp PC-E500), DS -HPCALC (HP11C & HP16C), some ports like Raptor, Cave Story mods and other little things...
I forgot to mention it but we can count the Famicom System Disk which is included with NesDS and also arcade game systems with S8DS.
So to summarize, you can run around 70 different systems on DS Lite more or less correctly with an R4
You can find all this on the forum and on GameBrew
https://www.gamebrew.org/wiki/List_of_DS_homebrew_applications