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

However, they do have a significant goth influence and even have some goth songs in their repertoire, like "Diener eines Geistes" and "Erinnerung".

If you want to dive into the goth music scene, some of the bands that might appeal to you if you enjoy Lacrimosa are Dead Can Dance, Love Like Blood, and Mors Syphilitica.