What and where is Lexington's New Street?

Map of Downtown Lexington, Ky. (LexingtonKY.gov)
On my lunch walk yesterday, I found myself at one end of my favorite streets in downtown Lexington: New Street. Or what I thought was its end.

This little one block road reminds me of a narrow way in Boston which in itself conjures up imagery of our nation's colonial history. I've also been fond of this little road and I've mentioned it once before following a BGT deTour of Clyde Carpenter's carriage house:
Every time I pass down Lexington's New Street, a one block path between North Mill and North Broadway, I am taken away to the narrow, history-filled streets of Boston, Mass. The narrow street, nestled between a busy road and beautiful Gratz Park, has a variety of architectural styles -- all relatively traditional -- that are perfectly scaled to the street's width. Adaptive reuse and infill are the common themes on this one-block stretch.
So you can only imagine my surprise when my eyes gazed across North Broadway and I found this:

Opposite New Street on the west side of North Broadway is a street sign which appears to suggest that New Street crosses North Broadway. Why else would a street sign for New Street otherwise exist on the west side of North Broadway to mark New Street? A turn from Broadway onto New is illegal; do not enter signs flank both sides of New Street.

Adjacent to the street signage, a narrow alley empties into a parking lot. And behind the parking lot, a very large grassy area. A chain link fence on the parking lot's northern boundary is all that separates the lot and this "extension of New Street" from Morrow Alley. Could I have found the vestiges of another of Lexington's alleyway connections?

If I did, I am now doubtful. The evidence is against me. Lexington's official maps and GIS recognize New Street as being only one block from Mill to Broadway. It has been this way since at least 1886 as a review of five sets of Sanborn insurance maps confirms.

Perhaps this is just the case of a driveway and very poor street signage? Probably so, but it's always worth investigating. And I'm glad my suspitions were incorrect as New Street - in only one block - remains one of my favorite in Lexington.

I still have one unanswered question, though. Why is it called New Street?