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Samael, among the oldest of his angelic siblings as an Archangel, has hardcore flock instincts because I headcanon that angels are a very social species similar to humans, and are like a flock species in particular. So Samael, as one of the oldest angels, gets to watch over the fledglings as they're born along with his fellow archangels like Amenadiel since I doubt Micheal was ever interested in fledgling-rearing. And he raises his siblings, as God and the Goddess are too busy with each other or projects (humanity), so it falls onto the archangels to raise the angels. Preening is a very social activity, done to strengthen a flock's bond. If a fledgling isn't part of such activities, they become socially stunted.
Samael raises many of his siblings, but then the Rebellion happens. He Falls, alone and banished to Hell. Samael burns away in the Lakes of Fire, and Lucifer is what emerged. Lucifer, no longer an archangel but something more infernal than celestial. I headcanon that demons, the opposite of angels, are incredibly solitary creatures, meaning Lucifer is completely alone. He tells himself that his pesky flock instincts burned away along with Samael, but he's lying to himself.
In the time it takes for him to establish his rule as King of Hell, he meets Mazikeen. At first, he trusts her as much as he trusts any demon; which is to say, not at all. But her determination and her loyalty is enough for Lucifer to begin trusting in her, confiding in her. She, as a demon, can't understand how lonely he feels nor how much he yearns to have a fledgling to preen, but sometimes when the longing gets too much, she'll very reluctantly allow him to preen her, braid her hair, whatever Lucifer needs to feel better. And sometimes, just sometimes, Lucifer would even allow Maze to help him with his wings. He would allow her to preen his feathers, trusting her not to stab him while his back is turned.
And then he ends up in LA, and Lucifer is firmly shoving down any itch he might have to form a flock of his own. He surrounds himself with people, day in and day out, and it feels like everyone leaves with a little piece of his heart but it's fine. He is fine. He feels hollow, his bed feels icy cold no matter how many bodies warm it, and he feels the loss of his wings every day through phantom pains but it's fine. He's been without a flock for eons, he'll survive. He's been surviving.
And then he meets Detective Chloe Decker. At first, he sees her the same as he does anyone else; an inevitable conquest and perhaps an ally in hunting down Delilah's killer. But then the case is over, Chloe is immune to his charms and Lucifer is...intrigued. He forces himself onto more of her cases, makes himself into a Civilian Consultant and somewhere along the way, Chloe becomes something else. Special. He trusts her in a way he trusts almost no one else, save Maze.
When he first met Chloe's daughter, Trixie, he avoided her for fear of being reminded too much of the fledglings he's raised as Samael, the fledglings that grew to be angels who stood by and watched as he was cast out of the Silver City. He tensed at her touch and did what he could to avoid her; every other time he'd come to earth, he avoided children for the same reason. But Trixie is a large part of Chloe's life, and he can't avoid her forever. The closer he gets with Chloe, the more time he's forced to spend with Trixie. Chloe is a packaged deal with her daughter, Lucifer can see how much she loves her daughter.
He gets invited to family game night, and the whole time Lucifer is struggling to push down those pesky flock instincts because he's been alone for so long that he should be used to it. He shouldn't feel such a strong desire to scoop Trixie up, hold her close against his chest and close his wings around them both. He shouldn't want to run his fingers through her messy hair until it's untangled and soft. He shouldn't want to sing her to sleep like he did for so many of his younger siblings. He shouldn't want to tuck her beneath his wings on dark nights so she could see how his feathers glow with starlight, the same light that he used to ignite his beloved stars. He shouldn't want any of that, because looking at Trixie hurts; she reminds him so much of many of his younger siblings, Azrael most of all. His favorite little sister, his Rae-Rae. He shouldn't want to take care of her the way he did for his siblings, especially since his wings are gone and never coming back, but... she's so small.
She's so small, and humans are so fragile, and Chloe means so much to Lucifer and Trixie means the world to Chloe.
Chloe, who at this point trusts Lucifer with her life. He's eccentric and insane and sometimes acts like he's never seen a human before but he's always there when she needs him and she's a detective, it's her job to be observant so she sees the way he looks at Trixie sometimes when she has to pick her daughter up from school. Glances filled with so much pain and longing that it breaks her heart. If it were anyone else, perhaps she'd be more wary that they'd look at her daughter like that. But she trusts Lucifer, she knows he would never hurt her or her daughter, knows Trixie would be safe with him. Chloe knows that even if she doubted hi,, all she'd need to do was ask for his word that he'd keep her safe and Lucifer would comply. She's seen time and time again, on several cases, that his word is his bond and that he would never go back on it. She trusts Lucifer enough to be indebted to him; after he didn't sleep with her when she was drunk, Chloe trusts that if she were to owe him a favor, he wouldn't ask her to do anything sexual at least.
So when one day she's needed for something or other, but Lucifer isn't, she asks him to babysit as Trixie's usual sitter is also occupied. And Lucifer looks at her so panicked, asking if she's really sure he's the best fit but she trusts him so much, and she's in a rush so he agrees. And from there, it's instinct. He cooks breakfast, picks out Trixie's outfit, he takes her to the park. When she falls and scrapes her knees, it's instinct to scoop her up and finally hold her to his chest like he's wanted to do for so long, and she fits so perfectly. And Trixie loves Lucifer, loves when he's around because he's funny and he's so nice to her, and he makes her mom so happy. She makes sure to tell Chloe every detail of the day after Lucifer's returned to his penthouse and Chloe is just left with this warm, fuzzy feeling in her chest as she sees how happy Trixie was in Lucifer's care.
That day was like a green light for Chloe afterwards. Whenever she needs childcare, she goes to Lucifer. Lucifer, who's more than happy to drop everything for the chance at getting to spend time with Trixie. It's the first time he's felt so happy in eons, the first time he hasn't felt like a piece of his soul is missing since he was Banished, since he Fell. Lucifer starts spending more and more time with Trixie and Chloe, starts spending more time at Chloe's house; he cooks for them, buys Trixie new clothes when Chloe allows it, he does her hair, he sings for her, carries her, holds her close. The more time he spends with the Decker girls, the easier nicknames fall from his lips for them. Darling, sweetheart, love, beloved child, it becomes second nature. He doesn't even have to think about how he hardly calls Trixie by her name anymore, especially since he was never in the habit of calling Chloe by her given name either.
He doesn't even realize they've become his flock until Amenadiel points it out, tentatively so Lucifer doesn't spook and run. Lucifer, who couldn't even run away if he wanted to because his instincts physically will not allow him to abandon his flock, struggles to process that he's allowed himself to indulge those instincts he hated so much to such a degree. But he can't even put distance between him and his girls, couldn't dream of leaving them. He's literally forced to confront the fact that he's made his own little family and there's nothing he could do but settle in with them again. Chloe was afraid he'd run when he realized how domestic he was becoming only to be surprised that he didn't, even if he was acting weirder than usual while he came to terms with the fact that he had a flock again.
(obviously Linda, Amenadiel, Ella, Charlie, Dan (who doesn't die because I say so), Eve (eventually), Maze (when she's developed a soul), and Rory (when she's born) also become parts of his flock. Amenadiel is the happiest about it, because when he Fell he was also cut off from his old angelic flock and felt the loss like the loss of a piece of his soul. It makes him understand Lucifer better when he realizes Lucifer was without a flock since he was cast out. Maze also understands Lucifer better after she gains a soul and goes through the whole spectrum of human emotion. It feels like a slap to the face when she realizes that even with a soul, she'll never truly understand what it's like to be a social creature cut off from your species; she's still a demon at the end of the day, still a solitary creature. But after facing loss and hurt and depression and grief, she understands Lucifer a little bit better and it might make her wish she'd been more indulgent of his flock instincts in the past. )