Lying means to make a statement that you believe to be untrue. LLMs don’t believe things, so they can’t lie.
I haven’t had the pleasure of one of these phone systems yet. I think I’d still be more irritated by a human fake apology because the company is abusing two people for that.
At any rate, I didn’t mean for it to be some sort of contest, more of a lament that modern customer service is a garbage fire in many ways and I dream of forcing the sociopaths who design these systems to suffer their own handiwork.