I assume by focus you mean manual focus?
I have just tested and if I set the Control Ring to OFF in the settings and then set the focus switch to manual, then I can use the Zoom Lever (top of camera) to Zoom in and out and use the Control Ring to manually focus (with MF Assist + Peaking etc) - tried in A, P, M and S mode.
If I set the Control Ring to Zoom in the settings and set focus switch to Manual, the Control Ring still acts as manual focus, with the Zoom Lever for zooming.
Even in iA mode, if manual focus is selected the Control Ring does the focus and the Zoom Lever the zooming.
In other words, whenever manual Focus mode is selected, the Control ring is used to adjust focus.
When in Autofocus mode, the function of the Control ring can vary depending on your settings. It can be left to Default in which case it function depends on whether you are in A,P,S,M mode. e.g. in S and M the control ring selects shutter speeds not covered by the S dial. In iA and P mode it operates the Step Zoom etc. You can override the Default behaviour and set the Control Ring to adjust ISO, zoom, WB etc.
Hope this helps. If like me you find the official manual clear as mud, you may want to invest in the
LX100 guide on Amazon - the Kindle version is now only £4.54.
I would off course be happy to answer any further questions - if I can - but you may find the above far more helpful in your purchase decision making.
Cheers!