Things are awkward in the apt world while apt-key is deprecated and things like Launchpad and general PPA usage are in flux.
This snippet attempts to replicate add-apt-repository functionality for sanity, probably quite badly. There's no error checking or anything advanced, but at least the script is easy to understand.
Syntax: [sudo] addaptrepo.sh <repo-string> <gpg-key-fingerprint>
Then follow up with [sudo] apt-get update. I'm not making that call for you :P
You can find the gpg key fingerprint for a Launchpad repo by expanding Technical details about this PPA.