No sorry, that's not the case. "Lỗi" means "fault" or "mistake". I get this all the time when I was a kid.
My parents would ask me "con (parent referring to child) biết lỗi không?" which basically means "do you know what you did wrong?". To which, I say yes ("dạ Ba Mẹ"), and ask for their forgiveness:
"Con xin lỗi. Ba Mẹ tha lỗi cho con không?" = "I'm sorry. Do you (my parents) forgive me?"
By saying "xin lỗi", you're practically asking someone to excuse your faults. That's also why "excuse me" is a good translation too, depending on the context.
Please keep in mind that I speak with a southern dialect. I can't confirm what a northerner would say. I hope that helps!