Question

1. He cannot have told a lie.
2. It is impossible that he told a lie.
(#1 mean #2. Right?)
3. He could not have told a lie.
(What about #3? What is the difference between #1 and #3? What is the meaning of #3?)

Answer 1

1 and 2 mean the same thing, yes.

3 means the speaker does not believe he would lie, but it's a belief, not a fact.