It doesn't count down in lobby or GH, I used that trick when I was PLing my toons AA's when OMM missions gave XP and lesson worked on tasks. I'd run LOTD on the toons in the missions as well as the bots/alts parked in the lobby. I got out of the MM, requested and got back in, then did my afk. It worked out so I could wait in the lobby and CF back to do another round of tasks later with the same lesson on. I'm very interested in this FS XP for being able to play my sham who has max aa and share the xp so that the cleric on the same account will get xp. That way, I get my slower back and my awesome cleric gets to AA still. They didn't say how much xp is taken from you who is sharing it, so I'm guessing 20% like LAA possibly.
Side note, you may know this already but they allow task wins to gain double on double xp weekends. So it reverts back to how things used to be, which is nice if you run and save 10 tasks before the weekend of double xp. It's helped me max aa on several toons.