So far, the name Lilith has had plenty of callbacks to witches, monsters, and other evil creatures. That may give some people pause when choosing the name.
However, let us remember the Lilith placement in astrology. Such a thing refers to how you go against the grain of society and how you defy norms.
While Lilith does refer to a witch or demon, it also refers to a woman who tried to forge her own path. When people ask you why you named your child Lilith, refer them to that meaning.
That same meaning might give the child some confidence later.