Reaction between lye and water?
The fumes will contain trace amounts of NaOH. The fumes are microscopic water droplets, and these droplets will still be caustic, as they are essentially a solution of sodium hydroxide.

There is no real chemical reaction going on here, but rather a dissociation of the sodium and hydroxide ions, which is an exothermic process. Solid sodium hydroxide is 'hazardous', the resulting solution is 'hazardous' and the fumes above the dissolving lye are 'hazardous'.