To force a new DHCP lease on OS X you can use the following:
sudo ipconfig set en0 BOOTP; sleep 1; sudo ipconfig set en0 DHCP
It basically tells the ethernet device to use BOOTP, which gets rid of the current IP, then tells it to use DHCP a second later, which makes it request one again.
The device, above
en0, should be changed to whatever device is to be updated.