Because I'm still working out how Rika's head works in some ways, and because Lambda's essay made me think about some things.
So the thing about Rika is that I think love and hate is tangled together in her head in a very fundamental way. The very same people Rika loves the most are generally the same people she's been given most reason to hate. Lambda's just the latest example of that trend, really - it's something that's existed in some sense for the entirety of Rika's life, because Rika has always half-hated her mother, because her mother didn't believe in her "imaginary friend", and when given the choice between her mother and Hanyuu, Rika will pick Hanyuu every single time, and justify it to herself by hating her mother. This has been amplified over the years by repeating a cycle of events that frequently ends in her best friends going nuts and killing and torturing all their friends including her, but even if Rika had never died, I think she would have had gigantic mother issues.
I think a lot of this is why Rika is a bit of a sadist? Rika is really complicated about it, but in general, the second she no longer has to worry about consequences, she is screwing with people's minds, and her teasing in general has an edge of friendly sadism to it. I'd say there's two major factors in it: One, Rika is generally in a constant state of powerlessness. Amping up the creepy child factor and making people hurt is one of the few ways she gets any degree of power. She's a ten year old girl; no one listens to her unless Rika gives them a strong and pressing reason to. And the quickest and most effective way of doing that is to be creepy. Two is that Rika actually is a sadist, in the technical term of the word. She just does like hurting people. I mean, she's not as extreme about it as, say, Bern, but that's mostly because Bern doesn't care about consequences to the people she hurts. Rika has to, and also she's not so broken that she doesn't want to. So there's a much stronger element of play in her sadism? With Bern, any element of play is more like a cat slowly flaying a mouse. With Rika, it's more like two cats playing with each other. And I do think that the fact that love and hate have been intermingled for so long for Rika is part of what created that in her originally. It started as a way to equalize herself with people, and ended as a way to give her power. And Rika thinks power is delicious.
And the funny thing to me is-okay, Lambda mentioned in her essay that Lambda hates it when Rika hurts her because it's something separate from love to Rika. Except while it usually is for Rika, it isn't always when she's dealing with Lambda? Some of the moments I've gone to myself "wow, you're really gay for Lambda, Rika" are when she's hurting Lambda. And it ties into the whole powerless sadist thing, really. Rika loves the fact that Lambda will let her hurt her sometimes. Not...entirely because she thinks Lambda's cute when suffering, although that's yeah an aspect of it and she does like the trust and domination aspect of it. But also because it's one of the few times Rika's been on that end of hurting, and a part of her really, really enjoys that. It's the whole while you're throwing someone else into a cage, you're reminded that you're not the one in it thing from Umineko. And Rika knows that she couldn't do that to Lambda if Lambda weren't willing to? So for her it's almost a present, and it's one that Rika really likes. I mean, it's not a good habit for her to get into? I mean, yes, there are plenty of people who can practice BDSM safely and sanely, and that's really pretty much what it's about at the core even if Rika doesn't realize it, but I don't really think anyone's going to say a three quarters trauma crazy loli is going to be one of them, especially not with a relationship as inherently fraught as hers with Lambda.
How this ties into the red thread event is more complicated. But it's safe to say that Rika spent a lot of time avoiding Lambda on it when she could, and hurting Lambda when she couldn't. Lambda interpreted this as Rika hating Lambda enough that it outweighed what love Rika has for her when Rika's crazy enough to show her real feelings. ...While there can be an element of truth there, definitely, it's really not the full truth. In an environment where Rika had her friends from home here? Maybe it would be true, idk. I don't think Lambda's usually all that damaging to her, because I think in the end she falls enough into Rika's normal coping mechanisms that Rika can handle her, but she can definitely be a distraction from Rika finding friends who aren't as damaging. But I don't think only nondamaging friends would be entirely good for her, because Rika lies so constantly and with so many layers that it takes a screwed up relationship for her to have someone she can be honest around. In a lot of ways, Rika's relationship with Lambda is closest to her relationship with Hanyuu, with all the insane codependence that implies.
But basically during the red thread event, Rika was running really hot and cold towards Lambda, but mostly cold. First, she avoided Lambda. This is complicated reasoning, and I'm still not really sure it was the right play decision, but...hmm. I think a lot of it was born out of the fact that Rika doesn't like being dependent on people. She is dependent on people! Fundamentally, for her sanity, for any chance of survival, etc., she's dependent on a lot of people. Hell, I'd say she's so dependent on Hanyuu that it reaches the codependent stage. ...But she hates it. She wants to be strong enough that she doesn't have to be dependent on people! Especially because love and hate run so closely in Rika's experience.
And with Lambda- Okay, Rika likes Lambda. Rika is in fact a little in love with Lambda. But Rika does not want to be dependent on her in particular more than almost anyone else! This comes down to, basically, the fact that Lambda is one of the few people Rika can't really separate her love and her hate for, and is, in particular, someone who has proved herself...not really dependable? I MEAN she is for Rika more than anyone else, but she'll tell Rika no and put her back into her hell without any major qualms and generally she's just never gotten to the point where Rika trusts her to do anything more than what she extrapolates from Lambda's general behavioral patterns. Which isn't trust so much as predictions. And making Rika suddenly vastly more dependent on someone who she doesn't trust in a way compatible with red thread, and with her general issues about desiring to be in charge and the way she tends to accept what Lambda tells her because she's a witch and unless it's really worth fighting over it's not worth fighting... yeah, she DID NOT WANT. And at least avoiding Lambda made her have to follow her which meant that Rika had a little more dominance of the situation! Except not really because that just drove Lambda more nuts, which made Rika try harder to control the situation which...okay, in general that's the kind of insanity loop Rika is really good at recognizing and trying to figure out ways to head it off? I mean, canon is all about her trying to prevent insanity from reaching the loop point seriously. But not when she's crazy too.
And then when Lambda caught up, Rika kept making Lambda think she hated her! ...Really this had more to do with the fact that when the full red thread event was in place, Lambda kept being on the edge of torturing her. And Rika...has experienced that! A lot! TRAUMA'D LOLI FACING MORE TRAUMA :( (And by :( I mean I totally want to do that more.) And usually in that situation, she mindfucks because that's almost the only defense she has, and if she's going to hurt then goddamn she's going to do her best to hurt the person responsible back and maybe even out of hurting her! And she did, and because she was crazy at the time and both loves and hates Lambda at the best of times, she did so viciously enough to actually hurt Lambda WHOOPS. Except not really whoops because she enjoyed hurting her when she was crazy because of the whole sadist/power thing. But whoops afterward.