What certificates and/or files are needed to bypass iOS's passcode lock?
The complete description of the feature on the Lantern site is "Pass code bypass with certificate file from syncing computer" so I don't think "until the device is unlocked" is the accurate way to phrase it. It seems that Lantern re-uses the pre-existing credentials set up between the computer and the phone.

edit: And in re-reading your question it seems you may be aware of this. A quick perusal of the iOS developer documentation doesn't yield anything to me but you can likely determine this for yourself if you have a mac you sync your phone to.

from a terminal window run the command sudo fs_usage -wf filesys | grep -i itunes and you should be able to see what files iTunes consults when you connect your passcode-locked phone.