I have successfully imaged several Dell models with the I219-LM NIC including the 7440 AIO. I don't have access to the hardware to check at the moment, but I have seen the Optiplex 7040, Latitude 7270, Latitude 7470 and Precision Tower 3420 which I believe all have this NIC and the driver worked for all of them. Here is a link to the driver download that worked for us: https://downloadcenter.intel.com/download/22283/Intel-Ethernet-Adapters-Connections-CD I have used this driver in our WinPE 5 x64 boot image using DS 7.1 and WinPE 10 x64 boot image in GSS. I have not tested the x86 version.
The driver that worked for me was PRO1000\Winx64\NDIS62\e1d62x64.inf
I have added it to our boot image using the built in Boot Disk Creator as well as injecting it into the existing boot image using DISM.
Hope that helps!
EDIT: I updated the path to the driver that worked for me, I accidently included the wrong location it is NDIS62 that worked, not NDIS64. Sorry about that!