The PI will automatically switch the cable config around IF the camera is powered up first so you will not need a cross over cable.
The issue is that the Pi will not have an IP address for the LAN connection.
The simplest way to set one is to configure this via the /etc/dhcpcd.conf file along these lines:
sudo nano /etc/dhcpcd.conf
You want the file contents to be similar to these
# Inform the DHCP server of our hostname for DDNS.
# Use the hardware address of the interface for the Client ID.
# Persist interface configuration when dhcpcd exits.
# Rapid commit support.
# A list of options to request from the DHCP server.
option domain_name_servers, domain_name, domain_search, host_name
# Respect the network MTU. This is applied to DHCP routes.
# A ServerID is required by RFC2131.
static domain_name_servers=22.214.171.124 126.96.36.199
The last three lines will need setting to values for your PI<->Camera network.
The last two lines may not actually be needed if only the Pi and camera are on the network.
This is only for IPv4
You also need to think how you will support the Pi without internet / network access - possibly WiFi?