Lucia is indeed pronounced Loo-CHEE-ah in Italian. It's occasionally pronounced LOO-cha as well if you want it to be the female form of
Lucio, but then it's got a stress on the u so that people don't pronounce it Loo-CHEE-ah.
The overall rule is that c followed by the letters a, o and u is pronounced "k" so you put a mute "i" to make the "ch" sound. So I suppose
Lucia is the exception here, at the moment I can't think of other words containt c+i+a/o/u where the "i" isn't mute.