From the perspective of the Lagre, quenching of a fire with water is really just starving it of air, after all - there are chemical fires that can't be stopped with water; starve a fire of air, and it will always stop burning. Similarly, heat (or absence of) changes water between forms. They used fire to boil water, to melt ice, and so on.
I figure "fire trumping water" is kind of an uncommon stance to take in an elemental system, but the elemental cycle is a very good reason for Lagres to persue science - after all, they're trying to understand why the cycle is how it is. Nature trumping Air would be something they wouldn't understand fully until the discovery of photosynthesis, for example.