If a new host connects to a LAN without a DHCP server, how does it receive an IP?
Behold the beauty of IPv6 - it has Stateless Address Autoconfiguration, defined in RFC 4862.
IPv4 has APIPA (RFC 3927) and obviously the option of manual configuration.
Note that for functional networking you likely will need more than just "an IP". Name resolution and service discovery likely need to be addressed as well. See Zeroconf for further details and references to real-world implementations.