Learn Russian: Немыслимо, чтобы он соврал, это чушь! - It's unthinkable that he lied, that's nonsense!

While чтобы usually means "in order to," it has a special use after expressions of strong doubt, denial, or impossibility. Because немыслимо (it is unthinkable) completely rejects the idea that he lied, Russian uses чтобы rather than что to introduce the subordinate clause. It acts a bit like the English subjunctive: "It is unthinkable that he should have lied."

Why is the past tense verb соврал required after чтобы? Could we use the future tense if we were talking about a future event?

No, you cannot. A strict grammatical rule in Russian is that чтобы can only ever be followed by the past tense or an infinitive. In this structure, it acts as a subjunctive marker, so it doesn't indicate literal past time in the way a normal past tense verb does. You would still use соврал here even if the context was about something happening tomorrow.

Could we use an infinitive (соврать) instead of он соврал?

Not in this sentence. You can only use an infinitive after чтобы if the subject of the main clause and the subordinate clause are the same. Here, the main clause is impersonal ("it is unthinkable"), but the subordinate clause has a specific subject, он (he). When the subject changes, you must use a noun or pronoun plus the past tense.

What is the nuance of using the perfective соврал instead of the imperfective врал?