Lava lakes mean multi-mile deep convection cells.

[halfeye]

Convection cells generally operate within the same phase, which means the stuff going up and stuff going down has to be separated - otherwise you just get rapid counter-current heat transfer and it equilibrates pretty quickly. Phase change is energy intensive enough to allow these to occupy the same space. On top of that the stuff going up isn't going up because of relative density; it's going up because of a pressure equilibrium between the fluid column and the pressurized fluid, Bernoulli equation style.

Essentially one of them needs a proper loop, one of them can be counter current flow through the same area because of different mechanisms, and that makes a big difference in terms of space needed.

I'm still not groking that. The way I see it, either you have one flow up and another down, or you have solids falling through a liquid stream that's going up, and the latter seems likely to be much more slow and turbulent, and turbulence takes a lot of room. I personally suspect gases are a big part of it, I'm not sure whether as bubbles or dissolved. The pressure gradient through the height of the liquid is presumably greater than with water, because rock is denser than water.