It does, which is famously why certain newspapers are/were loathe to use the word "lie" in connection with certain politicians. They knew certain utterances were untrue, but they had no evidence of intent. Without intent it's not a lie; it's just wrong.

I’ve seen it used both in that way[0], and in the sense of saying any false thing.

There’s also a gap between the two of lying by omission: on the one hand, “I swear to tell the truth the whole truth and nothing but the truth” is a situation where that clearly counts as a lie; on the other, if I go past a street preacher claiming the world is 6000 years old, I don’t consider failing to stop and tell him and his audience that he’s wrong to be a lie.

[0] I use the word the same way you do; As a further example, if you did believe that the moon is made of cheese, and you said that it wasn’t, that would be a lie.