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There's no way she would have lied to me.
Literal
She [topic-は] me [to-に] lie [object-を] told [no way-はずがない].
~はずがない is the strong epistemic negative — 'there's no way that X / it can't possibly be that X.' Built from はず ('expectation, the case that') + が + ない ('does not exist'), it asserts that X is impossible based on the speaker's reasoning, not on direct evidence. Compare ~はずだ ('should be, it must be') — the positive expectation. The whole pattern is reasoning-based: the speaker is saying 'given what I know about her, lying isn't a plausible explanation.'