I guess it depends on the conditions you dive in. If I compare my Sony RX100 Mark II to my Panasonic GX7 I know that at wide end there are two steps advantage for the Sony because of the faster lens at the same ISO
However the image quality is not better in the same dark conditions even if the GX7 uses higher ISO
The challenge in my opinion is more with dome ports that require you to shoot apertures of f/8 and smaller as that is really dark and you start having a base ISO of 800 even close to the surface
If you operate with a flat port or under lighting then this becomes irrelevant
What is clear is that for video the 12.7 Mp sensor cropped with multiaspect can compete with a cropped standard 16 Mp 4/3 sensor as obviously in both cases you use only part of the sensor but in the LX100 case the pixels are bigger
Also because of the less crop with the LX100 the lens resolution is more preserved than with the GH4
When you will house the LX100 behind a dome however you will have the same challenges of soft corners than on the GH4 and the better ISO performance will come up