I would never deploy ZD's using DHCP as you are asking for trouble!
I would set the ZD up with 2 x addresses:
1 x AP manager
1 x ZD Management
Note: If you are local to the ZD you can access the ZD via the second port using the ZD AP manager IP address anyway.
To obtain the IP you can simply use Wireshark and apply a filter:
You will eventually see the ARP from the ZD which will give you its IP address
Good Luck