No, Law of the Dawn is not a goth band, because they play Neoclassical Darkwave/Electronic, while goth music consists of Gothic Rock and its derived genres, like Deathrock, Darkwave, Ethereal Wave, and Coldwave.

If you want to dive into the goth music scene, some of the bands that might appeal to you if you enjoy Law of the Dawn are Collection d'Arnell-Andrea, Dead Can Dance, and Ľahká Múza.