Is it permissible to expose a lying manager who has accumulated salaries [owed to employees] and does not stop lying in his work, even if it causes him and his company significant losses?

It is permissible to warn people about a deceitful and lying manager who cheats people out of their money and in their dealings. This is because warning Muslims about evil and its proponents falls under the legitimate advice due to them, as stated in the Hadith (definition): "Religion is an-Nasiha (sincere advice)." And as An-Nawawi said in his commentary on the Hadith, sincere advice to the general Muslim populace includes warding off harm from them and defending their wealth and honor.