The reason Jeremiah was so obsessed with status and honor was because he failed his very first duty: Protecting Queen Marianne. Worst of all, he never quite udnerstood what happened because he was just rank-and-file grunt then. So he became dead-bent on climbing ranks until he had the power to prevent these kinds of tragedies. Except Clovis went and died on him too and he himself got Orange'd, which made him even more crazy.
Zero being lelouch meant that, despite how much as Lulu fucked him up, it was all for the sake of... the exact same thing he wanted to do: Avenge Marianne. And as a bonus point, the royal siblings he thought dead turned out to be alive.
In general, things worked pretty well for him, since now he's got the aid of the world's biggest terrorist in his vengeance, and to boot, he's the first ally Lelouch has ever gotten who shares his primary goals.