According to the Tale of Years, the Shadow fell on Numenor about SA1800, with the Ringwraiths first appearing about SA2251.
If we cross-reference this with the Line of Elros in UT (and ignore the error which CT draws attention to in note 10 - it doesn't seem relevant to this particular discussion anyway) we see the following happening inside this time-window:
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the Númenóreans in his service exacted heavy tribute from the men of the coasts of Middle-earth
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This provides one obvious source for the "three great lords": they were Númenóreans in service of the King (possibly quite high-ranking officials) involved in extracting this tribute, and Sauron lured them with the Rings and promises of more temporal power.
This is, of course, purely conjectural, but it seems to fit.
There is as far as I know absolutely nothing in Tolkien suggesting that the Witch-king himself was a Númenórean (aside from a note cited by Hammond and Scull that he was "probably" one). He could just as easily have been Haradrim or Easterling. There also seems no reason for him to have any particular grudge against Númenór aside from just carrying out his masters will.