With each flight they move the curtain to the position determined by operations. This is done part of the post cleaning crew check by the flight crew.
I was once sitting in row 12 of a 321 and the curtain was between row 11 and 12 (one row after the toilet bulkhead). only 5 C pax in the 7-8 rows ahead.
The purser came thru and shook her head and started chatting with the FA manning 2L. It seems they are strictly told to put the curtain where it says to be in the sheets the get handed before the legs begin. The instruction comes via telex into the cockpit from FRA. I asked her why they don't just move it to give space to Y pax if there are only a few C pax. She said, that common sense doesn't always make sense, as this maybe due to cargo loads and trim of the plane. LH carries a lot of commercial cargo in the holds of the 320series. That would explain the 'let's do what we are told by corporate' quip a previous poster got. 737s no cargo issues, but trim surely makes sense.
OS has a trim problem on their F70 and 100. On my regular hops FRA-SZG I was sitting with a LH captain who lives in SZG and we had a nice talk about the F70. It seems OS is stuck with them.