“put their necks to the work.” This idiomatic language compares people to oxen, who put their neck in the yoke so they can do work. If an ox will not take a yoke, it will not work, and that is the image here. The nobles considered themselves above the work, and perhaps did not even support it at all, so they refused to work.
“lords.” The Hebrew is plural, “lords.” Many scholars think this is the plural of majesty, and the “lord” is Nehemiah, which is why a number of versions read “lord” (cp. CJB; ESV; JPS; KJV), and that may be true. However, since the Hebrew is plural, it is at least as possible that it refers to all the “supervisors,” or even the work of God via Nehemiah and his officers.