While their relationship is often portrayed as very close and affectionate, their focus is primarily on aiding the Sailor Scouts and protecting the world from evil.
It's important to remember that Luna and Artemis are cats, and the show treats their relationship in a more platonic and familial way. They act as mentors and companions to the Sailor Scouts, and their primary focus is on their mission.
There might be moments that suggest a deeper bond, but there's no definitive "falling in love" scene in the anime.