As far as I know, "lesser" is just a shortening of "lesser platinum". Lessers got their name because the original platinum was a wild caught snake, and they had no idea what its genetics were. Breeding it resulted in snakes that looked sort of like daddy...but not all the way. Thus, they were "lesser platinums". The original snake became known as the "platty daddy", so when they figured out about the other gene that is needed to make the difference between lessers and platinums, it ended up being known as the daddy gene. So, lessers do not have the het daddy gene. If they did, then they'd be platinums, not lesser platinums.

As far as I know, the only other wild caught snake carrying the lesser gene is the one that was called "butter" because it was unknown at that time that lesser and butter are probably the same thing. So... in theory... all lessers, whether you call them lesser or lesser platinum, descend from the original platty daddy.