"To run a lab" means to manage and oversee all the activities and operations in a laboratory, such as conducting experiments, analyzing data, and supervising the lab members. Full definition
They will probably want to run lab work on your dog's blood and urine to ensure the kidneys aren't suffering any ill effects from the medication. (smartdogowners.com)
In my case, the senior fellowship means my salary along with that of two postdocs and the equipment and other costs of running a lab for 5 years. (sciencemag.org)
We recently ran some labs on my husband, and we did five labs, the poor guy. (blog.bulletproof.com)