I think it probably stems from, among other things, the fact that Alastor is constantly aware of Lucifer, in a way he isn’t of anyone else we’ve seen. He also makes it a point to get into his space when he avoids closeness with basically anyone else. The hand waves for example. The constant moving closer. The fact he shadows over to him, just to mess with him. It’s awareness. Alastor makes sure he’s subtle, but he puts himself around Lucifer, and engages in conversation with him, more than he ever needs to. When he doesn’t want to be around someone (unless he’s trapped by a deal, or working an angle) he makes it a point not to be. With Lucifer, for whatever reason, he’s different. He also never had a problem touching him, or being touched by him from the very first meet. For Alastor, all those things stand out in a big way.
That's the thing, Alastor rarely does even that.
He's shown little to no signs of being obsessed with Lucifer, or constantly going out of his way to be around Lucifer, or even starting conversations with Lucifer. Whenever they are in a conversation, Alastor doesn't even talk that much.
He also rarely touches Lucifer, unless you count their song in "Dad Beat Dad" but other than that? There is not any point that Alastor's hands are on Lucifer's body in season 2 other than when he was keeping Lucifer at arms-length in episode 1.
I went through the episodes and these are the examples used to prove Alastor's "obsession."
He approaches Lucifer in episode 1
He goes out of his way to annoy him and enjoys doing so, until he gets a rubber duck in the face LMAO.
2. Alastor's Duck-Season Mug
Which I don't see as him being any more obsessed than Lucifer seeing how Lucifer has a deer-season mug.
3. Alastor humming "Hell's Greatest Dad" after he quit.
Which I do find cute and it does intrigue me that that was the song he was humming.
Let's also keep in mind that Lucifer was the one that got him to quit. Lucifer was the one who drove Alastor out of the hotel. Not Charlie. Not any of the reporters or Vox's presence. LUCIFER was the straw that broke the camels back and look at how happy he is to be out of it all.
(Obligatory disclaimer thrown in cuz may as well: I don't hate this pairing. I ship Lucifer and Alastor. I've written plenty a fic about them, but COME ON guys, this is getting ridiculous).
Which I don't see Alastor very nonchalantly waving at Lucifer any implication that he's obsessed with him. He's not even verbally greeting him, it's essentially just a "sup."
That is the face of a man who is just chilling. He literally made no attempt to stop Lucifer from walking himself into a (very obvious) trap. Besides, it's not like Alastor chose to be there, Vox brought him there.
Also LMAO Alastor literally does not give a fuck that Lucifer is trapped in a glass jar. At most he looks amused and even that feels like its more from watching Lucifer get himself trapped and hearing him insult Vox than anything else.
4. The implication that Alastor stayed at the hotel for Lucifer
Look, lets be real, Alastor isn't staying at the hotel because he likes Lucifer or he's fond of him--and honestly, he has no reason to be. In the few scenes they were in together this season Lucifer has treated him like absolute shit.
Alastor is obviously cooking something up which doesn't imply he's obsessed with Lucifer, it just means he's planning something. He's not there because he NEEDS to be around Lucifer, Lucifer is just an element to whatever scheme is is brewing. I doubt Alastor is sticking around just to get to know him or be in his presence (once again Lucifer has been nothing but an absolute asshole to him).
And before anyone says anything, no this is not me painting Alastor as a poor baby angel who's just being picked on. Alastor's plenty rude in his own right, but point out one scene to me in season 2 when he was actively insulting Lucifer?
Lucifer on the other hand...
Those are the only times Alastor actively interacted with Lucifer. He's never even brought Lucifer up in conversation. He may step out of his way to annoy him, but it's not like Lucifer doesn't do the exact same. Lucifer does it more even.
Here are some examples for Lucifer:
When he goes to help Charlie with the reporters he looks directly at Alastor unprompted (Alastor is at the bar, not saying anything, just sitting there and observing just like everyone else).
"Hey, don't worry, Charlie, someone important is here to help."
He goes out of his way to bring Alastor into it when he didn't need to and Alastor merely responded by waving, completely unaffected. Lucifer could've very easily popped in to help out Charlie and pop back out, but nope, he had to make a dig at him.
2. Lucifers face the instant he sees Alastor
Look at him. The way he jolts up the moment he sees Alastor. Alastor went out of his way to annoy Lucifer in episode one, yes, but he has never lurched up in his seat at the sight of him.
3. Lucifer's deer-season mug
(if Alastor' mug gets to be used as an example for his obsession than so does Lucifer's).
4. The way Lucifer immediately started shit with Alastor, once again completely unprompted.
Lucifer: Oh! Look who it is interrupting this riveting conversation I was having with... Who are you again?
Alastor's response: You're still here?
Lucifer: Someone has to actually help out around here, Mr. Useless. What do you actually do here?
(Which is SO fucking ironic because Lucifer has done nothing to "help out" around the hotel, boy be fr)
All Alastor did was walk in the room, didn't even say anything, and Lucifer instantly zeroed in on him.
(Also are we ever going to address the casual disrespect Lucifer throws around people, especially at Alastor? "Someone important is here to help,," calling him Mr. Useless, dumb red loud-speaker. On that same note, have we heard Alastor say anything mean to Lucifer this season? Like actively rude or disrespectful? Any name calling? NOPE. Why do people treat Alastor like he's asshole in this relationship again? Lucifer's a fucking jerk).
4. Lucifer's "No Alastor's Allowed" sign
He went out of his way to put a sign up. Hell, he actually remembered Alastor's name, which we know he doesn't do with the rest of the Hazbin Crew, not in Vaggi's who is literally Charlie's (his daughter) girlfriend.
5. Alastor being the reason Lucifer got up to confront Vox
It took Vaggi bringing up Alastor for Lucifer to get up and do something about Vox. Not to help out Charlie. Not for the sake of the hotel. It was because he wanted to prove that he could handle the problem better than Alastor could.
"Oh, no, no, holda, holda, hold on, okay? I can handle any problem a-five hundred times better than that dumb, red loudspeaker, okay? "
Alastor was his motivation. (Which isn't entirely great considering that's your daughter, my guy. A megalomanic TV cult leader is running a smear campaign against your child, that should be reason enough).
6. Once again bringing Alastor into the conversation unprompted
Automatically assumes Alastor was the one who told Vox about his inability to hurt Sinners when at no point have we seen Lucifer tell him, nor have we had any implication that Alastor knew at all.
Vox: Lucifer. Lu! Lucy. Come on, buddy, we're past all that, remember? We both know you can't harm Sinners.
Lucifer: Uh-huh. Explains the showboating. Let me guess— uh, the bellhop told you that one.
The only person he told was Vaggi but he immediately assumed it was Alastor who spilled the beans. Instantly. No hesitation. No second thoughts. Alastor really is just lingering in the back of his head constantly istg.
As for Alastor lingering around Lucifer he really just...doesn't. The only time Alastor was even in Lucifer's personal space close enough to touch him was in episode one when he had his hand on Lucifer's head to keep him at arms-length. The only time he loomed over him was when he went to tease him in episode one and that wasn't even really looming, he was standing at full height. Up until Lucifer threw a duck at him, in which he bent down to glare at him, but otherwise that was it.
We've seen one time Alastor has gone out of his way to interact with Lucifer and that was in that single scene. The only other one that could possibly be brought up was when Alastor went into the lounge where Lucifer was, but like?? Him walking into a communal room to drink his coffee? Clearly unhappy to see Lucifer still there? I find it hard to believe.
Lucifer has shown to be the one who is hyperaware of Alastor's presence and LUCIFER is the one who goes out of his way to start conversations with Alastor. Alastor is not nearly as involved or obsessed with Lucifer people think he is.
And look, I know this is fandom. Fanon. Ships. Headcanons. Yada yada yada. Different scenes can be interpreted in different ways. People have there different headcanons; and sometimes people just want to have fun with the narrative. I get it. I understand. Can we just stop treating it like canon.
If there is anyone out of these two that are obsessed with the other throughout this season it was Lucifer hands down.
Never once did Lucifer come up in any scene of Alastor's unless they were literally in the same room. This perceived "obsession" Alastor has for Lucifer is so excessive and overblown I am begging people to go back and rewatch season 2.
