There's a few possibilities...
1) the lab sent the bill before the claim was submitted and/or processed by your insurance. This happens to me all the time, I think the providers just bill on a certain day of the month. I always wait for a second bill. The bill should actually show if there was a payment from the insurance company.
2) the lab used the wrong billing or diagnosis code to be considered "preventative." It happens. You'll need to get your doctor's office to provide the correct details to the lab, who can then resubmit the claim.
3) the doctor used a non-participating lab. You say you recently changed insurance. This happened to me once when I was literally one week into a new policy and didn't have the right card yet but I did have a letter from my company on letterhead with the correct info. Unfortunately, the doctor's office messed up and sent my sample to a lab that wasn't approved by the new insurance. I had to fight to get that one resolved but it was eventually.
I can check our claims online through my insurance company's website. I always know what has or hasn't cleared processing yet. My insurance company even told me once to never pay a bill from a provider until I receive the EOB (Explanation of Benefits) from the insurance company for that claim.
Good luck, I hope it resolves easily! Fighting insurance companies is never fun.