Here's an Update:

Had to remove the new rugs again, as they were kind of "dissolving" in the washing machine, and almost destroyed it. Had a hard time to get that machine running again (wet feet were included!!).

Now I brought out the old rugs again, and they have been peed on several times since. Luna is really bad with her litter box at the moment; worse than ever.

I think a part of this is also a behavioral issue; due to her constant bladder infections, she's not on good terms with the litter box. So she doesn't use her box for peeing and pooping at the same time. The second one always ends up on the floor. Setting up a second litter box for her did not help (Lily has her own box anyway).

But I got a new box for Luna yesterday; sometimes it helps to replace it from time to time.

Kirsten