"He lies" or "he is lying" for non-habitual actions

Solution 1:

The use of simple present tense with a non-stative verb is, as Rob notes, an indicator of Generic verb use.

He lies is generic, and indicates that the speaker believes that he is untrustworthy.

He lies, Nell. All the time; remember that when you go to his office.

It would not be said to anyone in reference to what he is saying at the present time, except with a screamer, in archaic or overacted dramas of the Dudley Doright sort.

He lies, Nell! Your horse is perfectly safe!

For real situations like this English uses the Progressive construction He's lying (virtually always contracted), which refers only to the ongoing present action.

He's lying, Nell. Look at the way he keeps watching the door.

Since the progressive can only apply to active verbs, and present tense generic uses are always active verbs, these two fit together nicely.

The issue doesn't come up with stative verbs like own, believe, or know.

He owns three buildings. She believes in Cthulhu. We know you're in there.

Since stative verbs are automatically continuous, there's no need for progressive (and it's ungrammatical), and since they don't refer to episodic events, there's no need to make a distinction between single and habitual events (and it isn't made).