Lucci ain't a Prince.
For the confused:
Generally, to be a CD, you need to be a king or a prince--although the WG can make you one if they want, like, they promised York.
To be a HK, you need to be both strong and be a CD. Loki fits the criterion, but Lucci doesn't. Strength isn't the primary criteria here, otherwise we should be looking at the admirals as the potential HK candidates, not Lucci.