To paraphrase a tagline from Superman - the Motion Picture
"You will believe a demon can cry."
Well, there is no denying it that Maze the demon has a full range of emotions beyond her usual hedonistic passions that are fulfilled by inflicting pleasure and pain on the damned. Correct me if I'm wrong, but I believe this is the first time we have seen the character produce tears. We know she was experiencing emotional hurt and jealousy over Ameninda (wasn't that Lucifer's contraction in this episode?) but it was expressed purely in anger and rage, which was probably the best she could do with her limited experience and emotional range at the time. Now we see a pure expression of sadness and despair at the knowledge that she will never be the most important thing in Lucifer's life. I felt quite sorry for the character in the scene.
The other inference that I take from these events, and I don't know that it has ever been made explicit before, is that Maze clearly is in love with Lucifer. Whether Lucifer created her with those feelings already in place, or he made her only to serve and she fell in love with him at some point since the dawn of mankind is unclear, but the depth of her feelings certainly seems clear to anyone paying attention, except the object of her affection himself, although it is quite possible he is simply not paying attention. In that way, all these other characters, both her intimate partners like Amenadiel and her besties like Linda and Chloe are really her consolation prizes, since she is denied the real relationship that she pines for.
I don't expect that the show will ever follow up on this or explore those feelings to some sort of conclusion, but TBH, I would be much more interested in watching a developing relationship between Lucifer and Mazikeen, compared to Lucifer and Chloe, which has just become completely stagnant and boring. OTOH, Lucifer lately has started to become as boring a character as Chloe, in the fact that the character simply won't grow at all in terms of his all-encompassing self-absorption. For any apparent step forward, the next episode shows two steps back. There may be an arc to the plot, but the two main characters have none. Meanwhile, we are seeing Maze, Linda, Amenadiel, Charlotte evolving significantly since they were first introduced, which is why they are all more interesting characters than the leads.
I know it's weird, but while composing this post, I had a Sopranos flashback, in that a major theme that emerged by the end of the series was "people don't change". Once a sociopathic mob boss, always a sociopathic mob boss. Once a selfish, narcissistic lord of hell, always a selfish, narcissistic lord of hell. In this case, it's not a very satisfying theme.