I am setting up a virtual test lab and I configured a domain controller VM running Windows 2008 R2 on my Hyper-V 2008 R2 server. I needed to download and install updates on it so I added an External NIC adapter and got that done. However, systems on my actual real physical domain were pulling IPs from this server and that was a big oopsy on my part so I immediately removed the External NIC adapter until I could find out how to go about keeping the Private and the External separate. If someone from the Server Fault community can help with this since I am pretty new to this, I would be very grateful. Thanks everyone.
I can't see any valid reason that you would need the DHCP service running in this lab so my suggestion would be to turn it off or remove that role.
That being said, if for some reason you do need the DHCP service in the lab environment then you'll need to isolate the lab network in order to prevent the DHCP broadcasts (during the DHCP DORA process) in the production network from reaching your lab VM by either putting the lab on an isolated switch or configuring a separate VLAN for the lab in your current switching environment. If you need internet access as well then that's going to entail some additional work at the router layer.
If you don't need internet access and don't need access to the production network then you can create an Internal virtual network in Hyper-V for Host and VM communication or a Private virtual network for VM only communication.