My thoughts:
First off, if Chloe agrees to help us, and Tanwen knows about it, that just means that Tanwen has that much more power from the debt, and therefore can ask for harder things if she wants. If we want to make this helpful for us, we would need to not let Tanwen find out that Chloe agreed to help us (rather difficult for Lirra), or only ask her for help after Tanwen tells us what she wants us to do (I think this is better, but has the problem that if the request is urgent we may not have enough time to ask Chloe).
Admittedly, if Tanwen wants something specific from us, she's unlikely to raise the difficulty level just because she can. In that case the only problem would be whether it drags Chloe into a situation that could be bad for her (like if Tanwen wants us to help fight a really tough monster. Or if she's not actually a dragon, and wants our help fighting the dragon we think killed those adventurers we pyred in the forest).
I really like the idea of getting her to stop us if it's something bad. A potential failure mode is if Tanwen finds out and tries to stop Chloe from stopping us. That could potentially put Chloe in danger.
Perhaps we could learn Mind Magic (or figure out how to lose specific memories from meditation?), and then erase our memory of asking Chloe to help or stop us? Come to think of it, with Mind Magic to alter what we believe is true, we could become the most believable lier in the academy. No one is going to doubt what the changeling says she saw with her own eyes. Not that I think we should do this for anything that isn't completely necessary(mostly because I like the characterization of Lirra as unable to lie), but it is an option if we ever need to out-bard a bard.
One more thing to note, is that if we do use deception in regards to Tanwen or our debt to her, it might have extremely bad effects on our relationship with her. One hypothesis is that she likes us because we are incapable of lying, so if she finds out that we deceived her, she might tell us to kill ourself and then she'll never trust anyone ever again. I'm not sure how likely it is that we would actually talk about whether we told anyone to stop us or not though, so maybe we'd be fine? If it doesn't come up anyway we might be able to get away with not wiping our memories of asking Chloe to stop us.
My recommendations:
Don't lie. As cool as I think my idea with the memory alteration is, it runs the risk of making Tanwen severely unhappy. I like Tanwen (though not as much as Chloe), and it's also a very bad idea to antagonize someone who can simply order you to die.
Determine how likely it is that Tanwen would ask us to do something that needs stopped. If we think she's likely to, strongly consider setting up Chloe as a sleeper agent, and decide whether lying is necessary to keep her safe. If Tanwen is not likely to ask us to do something bad, then I think we should wait until Tanwen tells us what we'll be doing, and ask Chloe for help(possibly just as a friend) if it is something difficult.
Inb4
Tanwen: *asks us to be her waifu*
Chloe:
Lucilia: