LX published policy is no partner awards in first at all, that's why the AP agent said they don't offer it. It's LH that offers F close in.
It seems like there's some sort of availability once a year or so, it's always called a system error. I would not be surprised if it was a system error, but I also wouldn't be surprised if it was just some unpublished intentional availability. Maybe it shuts up the enthusiasts (us) by having some random availability instead of none whatsoever.