Yes, I think this is a very strange interpretation of new Outpost - that it actually sets up an extra turn, and then checks whether it would be the 3rd turn in a row right before you start the turn. I don't see why it wouldn't be exactly like original Outpost: after the current turn, it checks whether it will give you an extra turn.
The new phrasing seems to support this even more than the original phrasing did. "Take an extra turn after this one (but not a 3rd turn in a row)" suggests that you only take the extra turn if it wouldn't be the 3rd in a row. Taking an extra turn means that an extra turn is set up. Exactly as GendoIkari said, Outpost does not say: "take an extra turn after this one. If this would be the 3rd turn in a row, skip it."
By the way, this Lich interaction applies to all these "extra turn" cards (except Possession), not just Outpost.
Donald X., maybe you missed this post since it was last on the first page? Seems like at least me, GendoIkari and Majiponi think that the wording on Outpost suggests that Lich can't skip the Outpost turn.
Outpost has to check if the turn will be a 3rd one right before that turn happens. If it checked any earlier, things could change such that you got a 3rd turn in a row; if it checked any later, the turn would have already happened.
Then, given that, how should it be phrased? Currently it's phrased to be clear and simple for people in normal situations, with the idea being that there's a rulebook (though currently there isn't, since the card hasn't been reprinted yet) to cover the tricky cases.
So then, there's two pieces here: generating the turn, and making sure it's not a 3rd one. We could spell these out as:
A) Take an additional turn after this one. When it's about to happen, if it would be a third turn in a row, get rid of it quietly.
B) After this turn, when you've got a moment, if another turn wouldn't be a third turn in a row, take one.
I went with A. I think you're arguing for B.
The card text is: "Take an extra turn after this one (but not a 3rd turn in a row)."
Leading with "Take an extra turn" makes it look like, okay we're taking a turn; now then, what else is there to say? But really we've provided timing and could rephrase it as:
"After this turn, take an extra turn (but not a 3rd turn in a row).
When you look at it like that, the uh amount of reasonableness of B goes up. B still is really seeing it as:
"After this turn, if it won't be a 3rd turn in a row, take an extra turn."
But then, the "if" has to come ahead of the actual turn.
So this does make it seem like Lich shouldn't be able to skip a 3rd turn generated by Outpost. There's no turn to skip until we know it's not a third one.