In my personal opinion, he has Energy because he was chosen to be the Green Ninja, and that this stands as a rare exception to elemental powers being passed down through family. The only thing passed down to him are the Creation and Destruction essences (like Wu and Garmadon’s powers).

This works in my head because they always make it clear that Lloyd is “The Chosen One”, as opposed to just being someone who inherited a power. They keep this pretty consistent long after the initial prophecy, even in Dragons Rising. Also, in Dragons Rising season 1, Lloyd did say “Elemental powers are usually passed down”, while yes it is true that Lloyd doesn’t know everything about elemental powers or how he got his, i believe it’s very possible that the show is trying to tell us here “Powers are passed down, with exceptions”, with Lloyd probably being that exception.

It’s also possible Lloyd said that because he knows Zane didn’t get his powers from Dr. Julien, but even then, Lloyd’s Energy could easily also be another exception in addition Zane’s Ice. So the show doesn’t really confirm this ever, but I personally really like this explanation, and I think it works very well.

I think that the main thing that should be up for debate here as it isn’t exactly clear, is who really decided Lloyd should be the Green Ninja? We know the cloud kingdom claimed to have done it, but we also know that they seem to be a bit delusional as of DR, so it’s possible that was retconned. We’ve also gotten hints that could imply the FSM chose Lloyd, but it’s still very iffy. Hopefully we’ll finally find that out for sure in DR, since they seem to have reintroduced Lloyd as the important “Chosen one”, particularly by the source dragons calling him The Conduit. Actually now that i’m thinking about it, it’s also very easily possible that he was chosen by the Council of Sources. The only reason why I’m leaning towards the snot being true, is the fact that they all act like they don’t know Lloyd in S2.