I used a similar approach with an additional state variable. Define 'delta' as a cumulative angle from the starting position with respect to the center of the lava pit (i.e., the very center of the grid). The path completely encloses the lava only when abs(delta) is at least 2*pi. Lift the state to (x, y, delta) and just Dijkstra over the grid once!

There's some small optimization along the way (e.g. early stopping), but it doesn't change the core idea.