No Kate likes to watch as well that was pretty much what the entire Julia/Nick questline was about. However, to add on to what you are saying Lisa
and I think that, in line with betting homework and dishes, it would be interesting if Kate, knowing that Lisa will get spanked naked for it, had her skip/do the dishes poorly and/or purposely fail her homework. If Lisa doesn't do as she is told then there is another penalty like having to sunbath naked to entice Max but without Ann finding out or walking around the block naked. If Lisa is a good girl and takes her spanking then she gets to be invited to join Kate and Alice on the show or in the pool. Kate and Max definitely get along and which is why she hasn't busted him for his show and instead has agreed to star on it regularly wearing nothing but an apron. So they definitely get along the only real question in the Kate/Max dynamic is who will be in charge of the household in the end Max or Kate. I think Kate should be the new Eric in Max's story to give the player a challenge to overcome and in Kate's story she should become the dom over a whole house of her very own sex slaves.