While I'm open to discussing the relationship between them, I have it by default where Lucifer loves Cathy just as much as he loved Charlie (especially due to her interest in the hellborn), they aren't as close as they were following Lilith's departure due to his similar Cathy looks to Lilith and that hurts Lucifer a bit.
Cathy is not fond of the sinners. Prior to season one, Cathy did not believe that the sinners could be redeemed. This is hell after all and a human must've done something wrong in life to be down here. Cathy knows that there are some sinners who are downright vile people who definitely deserve to be here. Despite how she feels about sinners, she isn't dismissive of Charlie's dream as everyone else seems to be as she knows how much it means to her. In fact, it was Cathy's idea for (my) Charlie to offer jobs at the hotel for lower class hellborn.