A few time I have personally disputed claims for so long that the provider simply gave up and zeroed the bill. I doubt that will work in this case since you have no personal affiliation with the lab.
In one case, my wife had gone for a routine breast exam and was advised to get another one. I called both the provider (my employer, a hospital) and the insurance company (my employer's own private insurance system) prior to her going and both told me it would be covered. Sadly, it wasn't. I wasn't surprised, since I hadn't really believed it would be, but I fought it tooth and nail since I had called and got confirmation that it would be. I was pissed. I kept calling back and emailing over months, telling them to check their phone records for my original calls where I was told it was covered. Finally, someone got tired of me and cancelled the charge.
My doctors routinely miss-bill routine wellness visits, Obama-care required 'free' services, such that I get small, annoying bills. I always dispute these and after some months they get covered. Having worked on the insurance end of it, I know very well what mistakes doctors make when coding. One example, every year I get billed for my cholesterol check, because they add a charge for the nurse to draw blood. Every year I call and complain and it gets dropped. I imagine they get a lot of money from people who don't know that this is an invalid billing, and don't know how to work the system. Drives me up the wall, to the extent that I skipped my last wellness checkup since I didn't want to deal with it again.
I wish you luck. Having seen insurance from both sides, it's a horrible mess.