Of course, the fact that Bellatrix killed Sirius renders any attempt at a relationship between her and Harry unrealistic, though it is interesting to see how some authors pull it off. A way around this is to argue that Bellatrix didn't mean to kill Sirius, that she used a non-fatal spell and didn't know what the veil was, and that her 'scream of triumph' was not really of triumph but of shock. But that's not the point I'm trying to argue here.
What is my point, then? It's that there exists, in some shape or form, an attraction between the characters of Harry Potter and Bellatrix Lestrange. I have compiled a list of the passages from the fifth book that can be interpreted as hinting in this direction. Bolding/emphasis is mine. All quotes have been taken from Harry Potter and the Order of the Phoenix, children's hardback Canadian edition (Bloomsbury-Raincoast). The page references between parentheses may differ slightly from other editions.
Let's see the first sequence that struck me as alluding to this theory:
'Lestrange ...' Harry said aloud. The name had stirred something in his memory; [...] though it gave him an odd, creeping sensation in the pit of his stomach.
Then Harry remembered. He had seen Bellatrix Lestrange inside Dumbledore's Pensieve [...]: a tall dark woman with heavily-lidded eyes, who had stood at her trial and proclaimed her continuing allegiance to Lord Voldemort, her pride that she had tried to find him after his downfall and her conviction that she would one day be rewarded for her loyalty. (106)
The 'creeping sensation' may have been JK Rowling's attempt at foreshadowing, but it seems unrealistic that Harry had an instinctive knowledge that this woman was going to do something terrible to his Godfather. How many 15-year-old boys have such presentiments?
When Harry sees the name Lestrange on the Black tapestry, he remembers not Rodolphus or Rabastan, both of whom he saw at the trial and who were also involved in the Longbottoms' torture, but only Bellatrix. And in what detail he remembers her! It's obvious that she made a strong impression on him the first time he 'saw' her, in Dumbledore's Penseive.
Yes, in that snippet, Harry certainly remembers her well. It's almost like he remembers her words by heart, which isn't the case for anything his friends say or the theories of magic he learns at Hogwarts. Additionally, we must remember that the books are written from Harry's point of view, and in the above description, the hatred and disgust Harry should logically be feeling towards someone like her – a Death Eater who tortured his friend's parents into insanity – is suspiciously absent. Harry doesn't even think of what she has done. Instead, he clearly recalls the words and emotions she expressed at her trial. There's something almost like wonder or admiration in this excerpt, which is supposed to be from Harry's mind.
And then there are the more blatant clues.
Their glass might be shattered, but still the little black-and-white people inside [the silver-framed family photographs] peered up at him haughtily, including – he felt a little jolt in his stomach – the dark, heavily-lidded woman whose trial he had witnessed in Dumbledore's Pensieve: Bellatrix Lestrange.(445-446)
If my memory is correct, that's the same reaction Harry had every time he looked at his first crush, Cho Chang.
But Harry's eyes were drawn to the picture of the witch. Her face had leapt out at him the moment he had seen the page. She had long, dark hair that looked unkempt and straggly in the picture, though he had seen it sleek, thick and shining. She glared up at him through heavily lidded eyes, an arrogant, disdainful smile playing around her thin mouth. Like Sirius, she retained vestiges of great good looks, but something – perhaps Azkaban – had taken most of her beauty. (480)
All right, there's no doubt here. We discover that Harry found her very beautiful at the trial, and even in the photo taken in Azkaban, where her appearance is unkempt, he still believes she is good-looking. He thinks Azkaban took most of her beauty - not all of it. The fact that she is Voldemort's most loyal Death Eater and the crimes she has committed do not deter Harry from admiring her appearance. Even more evidence toward this conclusion is provided later in the same scene:
Hermione nudged Harry and pointed at the headline over the pictures, which Harry, concentrating on Bellatrix, had not yet read. (481)
Concentrating on her. Why on earth would he be doing that? He has a newspaper in front of him and there's an article he considers important on the front page. Instead of reading it, he is distracted by the portrait of a beautiful witch and keeps staring at her, forgetting everything else.
Instead of looking at the girl he likes when they are on their first date, Harry's attention is, once again, caught by the picture of the female Death Eater. When he responds to Cho's attempt at conversation, his mind is obviously elsewhere and he tries clear it by taking a quick, absent-minded look around the street.
In the following excerpt, however, Harry doesn't seem to find Bellatrix attractive at all anymore. Considering the situation, that's not surprising. She is about to torture his best friend's sister, and Harry's head is filled with worry about Sirius and guilt for bringing his friends into danger, so he doesn't have the time to think about anything else.
The woman stepped forward, away from her fellows, and pulled off her hood. Azkaban had hollowed Bellatrix Lestrange's face, making it gaunt and skull-like, but it was alive with a feverish, fanatical glow. (691)
No, there is nothing here to suggest that Harry sees Bellatrix as anything more than a crazy, disgusting follower of Voldemort. For now, at least, because this doesn't negate that he did think of her in a different light earlier.
There's also the fact that Harry almost always refers to her by her first name in his thoughts, which isn't the case for other people he barely knows and loathes. It would be expected of him to think of her as Lestrange, Mrs Lestrange, or perhaps even 'Sirius's cousin', but not by her first name. Do we see Harry referring to Umbridge as 'Dolores' when he's thinking of her? Never. But when it comes to Bellatrix, he is doing it all the time: 'You'll have to smash this if you want to attack any of us,' he told Bellatrix; or 'What kind of prophecy?' repeated Bellatrix, the grin fading from her face, or even 'Shut your mouth!' Bellatrix shrieked and 'Get Potter!' shrieked Bellatrix, and she ran at him; he dodged her (691,703). Remember, the book is almost entirely written from Harry's point of view.
Even after she kills Sirius, Harry is still thinking of her as 'Bellatrix' instead of the expected 'Lestrange' or 'the woman' or even a more offensive word. When he chases her down to the Atrium, her progress is described through Harry's eyes as He wrenched open the door into the circular black hall and saw Bellatrix disappearing through a door on the other side and Bellatrix was almost at the telephone lift at the other end of the hall. (714)
It must be noted that the anger – no, the rage Harry experiences after Sirius's death is far beyond his years. We have seen his thoughts when he is angry at Snape – like the time he finds himself wishing he knew how to cast the Cruciatus Curse so that he could use it on Snape (GOF262) – but this time, his rage surpasses anything he has felt before. Actually, when he was faced with who he thought to be the man who betrayed his parents, in the Shrieking Shack, he did not have the courage to actually do anything, even though he wanted to kill Sirius to avenge his parents. His anger hadn't been strong enough, and once he had had the time to calm down, he even stopped Sirius and Remus from killing Peter.
In chapter thirty-six of OotP, however, we see proof that Bellatrix Lestrange is able to rile Harry to an extent of anger that goes beyond anything he has ever felt before. He is so angry with Bellatrix that he imitates her on two occasions: one is 'And he knows!' said Harry, with a mad laugh to match Bellatrix's own, and other is when he casts the Cruciatus Curse on her.
I could also point out that Harry's failure to succeed at the Cruciatus, to mean it, is meaningful in itself. He is unable to truly want to cause pain to this woman even though she is his Godfather's murderer. Is Harry's profoundly good and righteous nature behind this, or is there another (subconscious) reason, one he is not aware of?
Even Sirius's death doesn't seem to have killed Harry's strange fascination with the female Death Eater. When we read she was already back on her feet, breathless, no longer laughing (715) – how in the world does Harry know she is breathless when he's a good ten feet away from her, on the other side of the fountain? She hasn't spoken, so he can't have heard her breathlessness in her voice. So how does he know about it? Unless he has been watching her very, very attentively... If he hates her so much, he should be glaring at her in hatred and this hatred would cloud his perception, disinteresting him from other things such as the outward details of his surroundings.
'Don't waste your breath!' yelled Harry, his eyes screwed up against the pain in his scar, now more terrible than ever. 'He can't hear you from here!' (716)
Harry is in excruciating agony and it's very difficult and painful to speak when you are feeling that way. Yet when Bellatrix begins doing something that Harry probably takes for a sign of insanity (talking to someone who isn't there, or so he thinks, failing to interpret the pain in his scar as a sign of Voldemort's proximity), he takes the trouble of informing her of the futility of her actions. Usually, when I see an insane person doing something irrational, I don't bother pointing it out to them. And if the person had just killed someone I cared about, I definitely wouldn't bother advising them not to 'waste their breath'!
My theory is that Harry is, in a way, fascinated by Bellatrix Lestrange. He hates her, both before and after she kills Sirius, but he is also kind of mesmerised by her, as proven by his tendency to stare at her (or her picture) on every available occasion and his startling familiarity with her, demonstrated by his thinking of her as 'Bellatrix'. The fact that it is she who kills Sirius would make him feel even angrier, including with himself, for thinking that kind of thoughts about her. That's just a theory, though.
I'm not trying to convince you that he's in love with her or something like that, because that's ridiculous. But I like analysing (you can say overanalysing) characters, their behaviour and the possible motivations behind the behaviour. Besides, there have been more unrealistic pairings suggested in various fan communities, so why not give some thought to one that seems slightly canon-based, as unbelievable as it is that JK Rowling would [unintentionally] suggest such a thing? Then again, there are other things Rowling has written apparently without being aware of their implications or of how readers might interpret them.
I'm surprised that even the fans of the Harry/Bellatrix pairing (which, I insist, is highly improbable, but isn't that what fanfiction is for?) do not appear to have paid attention to these details in OotP, because I have yet to see one of them present the pairing in a canon-based way, which it is. But as I said, this is just a theory, and there are more absurd ones out there.