For the record lava tubes can happen in flood basalts; I've been to some at Hell's Half Acre in Idaho, and I'm sure there are others. But these are not like kar

For the record lava tubes can happen in flood basalts; I've been to some at Hell's Half Acre in Idaho, and I'm sure there are others. But these are not like karst-type cave systems; they're much shorter. It's really unlikely that the water goes anywhere other than the lake. It just might travel through a fracture network and seep out of the lake bottom miles away, but groundwater tends to flow broadly following the topographic slope (driven by the gravitational loading of groundwater surface called the 'hydraulic head') and there typically aren't isolated tunnels where some water can flow unimpeded by regional groundwater flow.