The only way for a duke to get named as a lord is if he assigns himself as a lord of a region in his own duchy. And no, he will not lose the duchy by naming himself as a a lord. That would be kind of silly.
But if he gets named Lord by another Duke, then he loses the Duke title?
That would make sense, of course. The disappearance of Imperial Regions makes it impossible for a Ruler to "re-populate" a duchy that has gone region-less. If there are workarounds, that would be quite nice.