I think Lila isn't out to ruin Adrien like she tries with Marinette because unlike Marinette, Adrien never said he would try to expose her. I think as long as you don't try to out her lies you're safe, like Adrien is, the moment you try something against her, like Marinette, Lila will destroy you. I think it's actually quite common for people like her, you're with her or not. You expose her or not. Adrien doesn't, he's safe. Marinette and Ladybug do, they're dead. The moment Adrien tries, amen.
I see what you mean, however, I think you’re missing one key factor about Lila’s character:
She doesn’t target those who try to expose her exclusively.
It is true that being called out on her lies, or just a liar in general is her berserk button, but that is not the only reason Lila dislikes Ladybug/Marinette, even Adrien.
As @kisilinramblings once pointed out in one of their analyses, what Lila hates the most is not being called a liar, but virtuous people.
In other words, Lila hates people who are better than her, more so if they are morally better than her.
The best example of this is in Chameleon, right before she grabbed the akuma. In the French dub, what she said to criticise Adrien and Ladybug could be (very freely) translated to: “I can’t stand people lecturing me.”
Which is exactly how she perceives Adrien’s attempt at reasoning with her; a lecture.
“Lila, I’d be perfectly happy being your friend, and I’ll gladly help you out with schoolwork…”
“Please, don’t lie to me like you did last time with Ladybug”
See? There’s literally nothing in that interaction that could’ve possibly be taken as an attempt to expose her. Adrien literally just asked her -in the nicest way possible, might I add- to stop lying. And then, the most he does is tell her that it’ll only get her in trouble.
He was just looking out for her and asking for perfectly reasonable things!
And what was her reaction?
Defending herself calling Ladybug the liar, literally asking him “Are you trying to be a superhero lecturing me just like Ladybug did?”, and then, rebuffing him.
Even so, what was her first reaction as Chameleon?
Targeting him to take his appearance and ruin his reputation in the process as petty revenge.
This clearly shows that Lila’s main target isn’t just people trying to expose her; it’s people who have more morals than her and that it shows they do.
This whole interaction just proves that Lila is incapable of acknowledging her mistakes even when she’s being called out on them in the nicest way possible. Where we, as the viewers, see Adrien being the cinnamon roll that he is and trying to help her out of genuine care and concern, Lila sees someone who’s trying to show he’s better than her.
She sees Adrien’s words as condescending.
Meaning the only reason why Lila doesn’t try to ruin Adrien is solely because of her interest in him and what he could give her.
For instance, if it weren’t for Gabriel meeting and making a deal with her, maybe she would’ve moved on from him after Oni-chan. Because, unlike in Chameleon, in their last interaction he was lecturing her for her lies and the consequences they’d brought on Nathalie and Gorilla!
He doesn’t even want to be touched by her!
On a side note, today I read an analysis on their interaction in “Ladybug.” And it pointed out something very interesting and very true; the moment Lila realises she’s been caught, just like the bathroom scene in Chameleon, she abandons her sweet persona entirely, and lets the aggressive one loose.
Which is reflected when she asks, “And why should I do that, Adrien?”
The thing is, even if she actually showed her true colours to Adrien, it’s not because he’d threatened to expose her. He literally said he didn’t know how. Lila was miffed because she was being reprimanded on her behaviour, again.
This hatred towards people who’re morally better than her is apparent in her distaste for Marinette. Sure, she hates Ladybug with a passion, too, but that does come from a mix of jealousy towards the attention and love the hero receives, and from the fact that she exposed her.
Marinette, on the other hand, did try to expose her lies, but even so, Lila gave her a chance. Meaning she was probably less mad at Marinette’s attempts than at her just and noble nature.
A kind of nature that grants Marinette the love, attention, and loyalty Lila so desperately seeks, especially from Adrien.
If we look back at Miraculer, it’s obvious Lila will try to take down whoever she considers an obstacle, regardless of the person’s interactions with her.
I mean, take Chloé and Nino!
Nino thinks she’s cool, and even tried to help her with her schoolwork when he found her looking dejected when they were walking to school in Oni-chan (although she did manipulate him…). And what does he get from that? Being badmouthed by her to Adrien’s father.
For once she didn’t even do anything to be disliked!
But it’s clear that the reason why Lila toyed with her emotions regarding Ladybug and their bond was because she was jealous of Chloé’s bond with Adrien. And nothing more.
So, I’d say the only thing keeping Adrien relatively safe from Lila is her, albeit shallow, crush on him. Because, when it comes to her, you’re either an adoring drone, or a nuisance she has to get rid of. And her judgement on who is what is completely arbitrary.