Testinstall

vim /etc/network/interfaces

auto lo
iface lo inet loopback

auto eth0
iface eth0 inet dhcp

# Ergänzung für eth1 (output interface)
auto eth1
iface eth1 inet static
        address 10.78.20.10
        netmask 255.255.255.0

apt-get install isc-dhcp-server

vim /etc/default/isc-dhcp-server

Ersetze

INTERFACES=""

gegen

INTERFACES="eth1"

vim /etc/dhcp/dhcpd.conf

ddns-update-style none;
option domain-name "test.local";
option domain-name-servers 10.78.20.10;
default-lease-time 600;
max-lease-time 7200;
log-facility local7;


subnet 10.78.20.0 netmask 255.255.255.0 {
  range 10.78.20.100 10.78.20.200;
  option routers 10.78.20.10;
}

systemctl restart isc-dhcp-server.service