Forgive me for asking, but what is this LapiLuci thing?
I'll assume it's related to the Lucia event, and my inadequate grasp of Japanese means I could not read all that delicious story.
It's canon that Lapis saved Lucia and Lucia is grateful to her. Lucia is the first human friend Lapis made and according to Lapi's affection dialogue, Lapis is very fond of Lucia.