Having revisted Miss Kobayashi's Dragon Maid, I'm reminded of all the discourse surrounding it's characters, Lucoa got the worst of it, not helped by Funimation's dodgy dubbing decisions, but I think Lucoa is better than you think.

Lucoa is a former goddess, in Aztec mythology, she is known as Quetzalcoatl and was banished from her position having been spiked by liquor and having an affair, loosely based on the actual myth of Quetzalcoatl.
After being summoned by Shouta, the mage boy, she remained with him, playing along with being his familiar because she felt at home, especially after seeing Tohru settle so well with Kobayashi, in fact each dragon seems to find their place pretty quick.
But one of Lucoa's most stand out roles is being the wise one amongst the cast, although she wouldn't step in the way of a battle, her clan prevents her from interfering but she holds a high enough presence that none of the other dragons would dare challenge her, you'll never see her angry but you'll also never see her fight.
One last thing to remember, in mythology, Quetzalcoatl helped create the world and by extension, humanity as well, so Lucoa really is more than just a bimbo dragon.