No, Lana Del Rey is not a goth artist, because they play Pop, 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 Lana Del Rey are Autumn's Grey Solace, Cocteau Twins, and The Cure.