I get 500k hits on Google on Norwegian web sites for "lure" and only around 100k hits for "undre".
Both words can be used to mean to ponder, to speculate, be ensurer whether something is true. "Å lure" has additional meanings such as to trick someone, to wait in hiding for someone/thing . I would hazard a guess that "lure" in Norwegian is etymologically related to "lure" in English.
"Å undre" is also used about being amazed, which "å lure" is not.
That makes sense, man: "å lure/to lure; å undre/to wonder." Isn't it amazing how two languages, separated by over two millennia can drift so far apart, yet still have so many similarities today? I wonder whether these similarities are due to that ancient connection or rather if it has more to do with the more recent contact in the early middle ages. Regardless, it's exciting to muse over... At least it is for me, but then, I'm a nerd =P
In the case of lure, it seems to have been borrowed from Middle Low German (spoken 1100-1600) or Middle High German (1050-1350), whereas both undre and wonder come from Proto-Germanic. The modern German cognate is lauern and the modern Dutch is loeren. Both mean to lurk or spy.
For some reason, I really want to say, " Hva undrer seg han over?" Is that grammatically incorrect or does it change the meaning? (It seems to me that I remember hearing earlier that the subject/object always comes before the reflexive pronoun in a question? Is that the case?)