I am working with the HP Z240 desktop workstations, but they also have the I219-LM NIC and it has been giving me troubles. My WinPE boot images were version 6.3.9600.16384, and the new 10.0.10586.0 images are now available with the Windows 10 ADK. It's been awhile since I updated my boot images, and I've done something wrong because my clients just spin and never get a PXE bootfile anymore.
Anyway, I would suggest checking your WinPE version, and I strongly suspect that a successful upgrade from 6.3.9600 to 10.0.10586 is going to be the answer.