People are already used to her bout of unpredictable, sparse visits in the headquarters, so her sudden disappearance in the Underworld for a few months or even years won't rouse curiosity, nor would it cause repercussions on her reputation and influence.
Her pregnancy would eventually be evident soon, and she'll have to make a gradual tactical retreat from the Underworld before the little bun grows from her womb.
Things in the Human Realm are a bit different, however. Although she doesn't make many appearances in public, she's still a public figure. She's bound to make an appearance outside familiar grounds and see people, such as in meetings and formal events.
Like the Fashion Week, for example. Fortunately, her baby bump isn't showing yet.
After she and Death called it a day and went to retire in their respective rooms, Lillie slept alone with her baby and Storm later that night.