Another approach you can take is simply making it so a violent resolution does not lead the players to accomplish their goals as well.
Trying to get information about a big nasty with a cult, and the players decide to just murder all the cult members? Well, the players might be able to beat the cult in a fight, but not fast enough to prevent the cult from burning their sacred texts, and now you have to piece info together out of the ashes.
This is a difficult line to walk: you have to plausibly present that the outcome would have been better if they had negotiated or infiltrated, versus just "well the DM was never going to give us the text anyway". You also have to make sure you don't just lock off the plot because they fought.
You need a clear backup plan that's just annoying enough to make it clear putting a little more thought into your first approach could have saved a lot of time., and maybe a slight downgrade of the end result of the plot (time is classic here, maybe a couple people the party was expecting to save got sacrificed while the party was messing around).
Technically the Mitflit has no penalty to its ability to see through a Lie: its Self-Loathing ability affects Will saves from Coerce, Demoralize, Make an Impression, and Request, and it's specifically flavored as self-loathing, so unless the bard is setting up the lie to attack their competence "You idiot, why are you attacking us? We're the emissaries sent by your boss" it doesn't really make sense to apply it. The flavor is very specifically that they're easy to bully because they hate themselves, so the bard nicely interacting with them doesn't work the same way.
From the Lie action block:
So ideally you'd just want to give them a large circumstance bonus for the pretty unbelievable lie, and let the dice decide.
Lie also has no Critical Success effect, the target either believes it or doesn't, so rolling particularly high above the DC doesn't do anything.
If the party does manage to succeed on the Lie with the circumstance bonus, I think TowardsTheFuture has it: you'd get a momentary cease-fire while they try and figure out what's going on, and the party would probably have to make additional lies to back it up. Going to check with the boss, resuming combat, and accepting your claims and doing what you tell them to might be on the table.