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.
hostname
# Use the hardware address of the interface for the Client ID.
clientid
# Persist interface configuration when dhcpcd exits.
persistent
# Rapid commit support.
option rapid_commit
# A list of options to request from the DHCP server.
option domain_name_servers, domain_name, domain_search, host_name
option classless_static_routes
# Respect the network MTU. This is applied to DHCP routes.
option interface_mtu
# A ServerID is required by RFC2131.
require dhcp_server_identifier
interface eth0
static ip_address=192.168.1.10/24
static routers=192.168.1.1
static domain_name_servers=1.1.1.1 208.67.220.220
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?