What happens when I print a 0,6mm thick wall with a 0,4mm diameter nozzle? The wall thickness is 1,2mm but the lip is only 0,6mm thick. How will the 0,4mm nozzle solve this?

Alternatively I could choose a 0,8 mm thick lip, but then the connecting end should be 0,4mm that is too thin.
I'd say you should experiment with Slic3r

it can manage extrusion in very sophisticated way

it can overextrude if you need a line wider than actual nozzle size
as same as it can underextrude if needed
it can even change extrusion continuously while extruding one line

here are simple examples






i use mattercontrol

take a look here - this is the same object the same layer and the same settings

please notice - this object has wall thicknes exactly 2 times nozzle diam

here is what i get with 


native MatterControl slicer engine which gives this slice

and Slic3r engine which gives this slice