It's not automatically obvious. There could (theoretically) be domestic gas fields that are solely supplying pipeline "islands" (connected to domestic gas powerplants and fertilizer factories) under long-running contracts. Those should/would be more stable in price, since liquefying that gas and selling it elsewhere would not be trivial.

But in reality, that's not the case for any large US gas fields. They are all connected to the national pipeline "grid", and their gas can go wherever it is most expensive right now.

But it's the case for e.g. many Russian gas fields. They are much more segmented, and they have nowhere close to the liquefaction infrastructure necessary to export a significant fraction of their total output on LNG carriers.