The books and TV series focus on the Baudelaire orphans and their adventures. While some characters may not conform to traditional gender roles, none are explicitly presented as genderless.
The closest you might get to this concept is perhaps with Count Olaf himself, who is often described as grotesque and unconcerned with traditional appearances. He constantly changes his appearance, and his gender can even be questioned when he disguises himself as the woman, "Shirley." However, Olaf is ultimately revealed to be male, and his constant transformations are more about deception than an exploration of gender identity.
It's important to remember that Lemony Snicket's "A Series of Unfortunate Events" was written in the late 90s and early 2000s, a time when discussions about gender identity weren't as prevalent as they are today. While the series is imaginative and often explores societal issues, it doesn't delve into the complexity of gender fluidity or non-binary identities in a way that is common in modern literature.