Looks like we're making some progress here:

Randi's idea to stroke cats with a wet cloth (due to the horrible heat wave we have) had a great side effect! I've tried it on my cats and thought I would start with Luna because it will do less harm to rub her scent on Lily than the other way around. And guess what happened? Luna lets Lily coming much closer and sniffs her, and when they just met in the hall, the sniffed each others' nose without growling. Of course they're still far from being best friends, but they're acting much better now!

Kirsten