Z-lining is frequently a timed ban... It may automatically expire after a few days or weeks. If it's a permanent ban you will have to contact the administrators of the IRC server that the Pub runs on and beg forgiveness. You might try logging into the pub from an IP that isn't banned and executing the command "/join #Services" and explaining your situation to one of the people in there.
As a side note, z-lines are automatic bans for what is considered extremely rude or disruptive behavior. Things like rapid nick changes, flooding, many logins from the same computer, acting like a bot, etc... Stuff like that is disruptive for everybody on the server, including plenty of people who have never heard of dropzone.com or the Pub.