Figured it out...
Log into the Live account that you purchased the DLC with first.
Start Lips.
Now log in with the second account with another controller and use that controller to navigate to Get Songs.
You should now be able to see and add the new songs to the second account's list.
Stupid, but it worked. Hope this helps somebody else.
Now I just need to figure out how to transfer the licenses to the 3 songs I downloaded to my other 360 to this one.
chili --
Enter the Pit