I was trying to see if the analysis board saves the PGN, and I don't see that it does. Maybe choosing "continue from here", but again idk if that initial pgn information is saved.
My suggestion is to use something like
Scid vs PC -
http://scidvspc.sourceforge.net/ - to make your pgn files and store games etc in a database
and since you are using a web interface I'm assuming you aren't using a personal PC when you are showing the games. So you can.
a) Use the Import game function (under tools menu) here on Lichess - prob best option for you.
b) use a portable program that doesn't require installation on whatever computer you are on (can be run from USB drive)
Lucas Chess (portable version available) -
http://www-lucaschess.rhcloud.com/indexTarrasch Chess Gui (same) -
http://www.triplehappy.com/*maybe someone has a better answer...