That's not totally true. Usually a lie by omission is implying something, and that something isn't true. It is deliberately instilling a sense of false knowledge. You didn't specifically say it, but you still conveyed it. It's still a lie.

Saying something sarcastic is not the same as saying it non-sarcastically, for example. What is conveyed is what's important, not what is said.

A deception is a lie though, they’re synonyms.