Hi and Welcome to YT!
My dog has LS. This link will give you info about LS, including symptoms. What you describe as your dog's odd behavior could also be something else like AAI, which is a malformation of the spine where it joins the head.
http://www.vet.utk.edu/clinical/sacs/shunt/faq.php
Initial basic bloodwork will tell if his liver enzymes are abnormal. If yes, a Bile Acid Test would be run. An Xray can determine the size of the liver: LS dogs tend to have small livers in relation to their body size.
An Xray can also determine any malformation of the spine. Until the spine is checked by Xray, it would be wise to keep him crated, and have this verified or ruled out ASAP, like tomorrow. This is a very critical condition, and would be wise to take care of this first.
The cost you have stated seems quite outrageous to me. I would call around, and save some money by going to a vet clinic or teaching hospital where a neurologist is on staff, or at least available for a consult, also so you don't have to run all over the place to get your pup diagnosed.