Normally, 1A and 1 K are blocked.
To get 2A or 2K, simply go to lufthansa's website, and go to the section 'manage my booking' and select your seat.
If it is blocked (like 1A or 1K), click on 'window' instead of selecting the seatmap, and with a bit of luck, within the minute you will get 1A or 1K.
If that still doesn't work, contact the LX call center and ask them and mention them that the seat is not taken.
They will tell you a bunch of nonsense such as the seat is blocked for HONs, or babies,...
Keep trying and it will work out.
I am talking out of experience for my recent flight HKG-ZRH in F.