Wow, I've never seen a photo of an LS with the US bars before, they are wide.
It will be a different bike with the low, narrow bars.
On my bike once the lever mounts and switches are installed there is almost no bar visible, no room for any accessories for sure. The master cylinder has less than 1/8" clearance to the black cowling around the speedo.
I have a top brake hose in my shed, someone asked for the length a few months back but I could measure it again if you want to get one made.
You could buy a complete set of braided s.s. lines for your bike, mine are from HEL but plenty of companies make them to suit the LS with low bars.
You will probably find you need a set of long stalk mirrors or fit a set of bar end mirrors. I used to have them but they get broken easily (even with the narrow bars), they wouldn't last on those wide bars.