Lameboy does save, but if you read the documentation, you'll find that after saving in-game you have to press X to send the updated save info to the *.sav file on your card. If you don't do this, you'll lose your progress. Pressing L+R to go back to the rom selection menu also automatically does this for you.
Judging by the date of that MaxConsole link, I'd say that's the old version of DSboy, not the newer one with palette support. IMO you'd be best off ignoring both, but I know that the one you're trying to use has no saving support whatsoever. Just use Lameboy instead.
I use an R4 and an EZFlash3-in-1. If you use the GBA ExpLoader on your R4's SD card it works fine with the EZFlash3-in-1 and will save if you do it right. After you're done playing a GBA game turn off your DS and turn it back on. Then go to the GBA ExpLoader again and it will ask you if you want to write to your SD card. Do so and your save you created while you were playing is now on the R4's SD card. Sadly you have to do this every time you are done playing a GBA game. If you don't then the save file will stay on the EZFlash3-in-1's RAM which wipes itself about an hour after the DS is turned off. So you must save it o the R4's SD card every time. On the other hand, it means that your save files are incredibly secure AND you can easily back them up on your computer.