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.