It consisted mainly of the steps in the photo, although there was a wee bit of road at the bottom of the lane before reaching King Street.
The building on the left of the steps photo (or to the right of the billboards on the top photo) was a stone engravers called Carnegie & Son. It's a place I remember passing on the bus regularly as a youngster because it's window display was made up of gravestones. No need to stop off there with your pocket money!
You can consult yesterdays map to find the location of William Lane. It was to the left of Dens brae, opposite Wellington Street.
I checked Google's satellite map, and if you zoom into the area you can still see the ghost of the steps showing through from the undergrowth.