One big difference between the two is that the LX100 doen not have full "zoom through" when using it's dome port or an external lens. It doesn't focus all the way out. The RX100IV does.
But in many other areas, the LX100 is easier to use, especially WB and does a great job with macro and CF/WA. I like it's menus and SW a lot better.
Just zoom with your fins!