Alice Morgan is an amoral character who has already murdered her parents for not particularly good reasons. She knows Luther thinks she is guilty but has not produced enough evidence. But he is a threat. But she also has a strange attraction to his character (this becomes much more obvious in later episodes).
So there are several plausible reasons why she attacks and lies to Zoe.
One is to put emotional pressure on Luther (he might be removed from the case if he becomes too involved and his boss knows it). At the very least it would impair his judgement. Telling fibs to Zoe may, indirectly, cause her to put emotional pressure on Luther: attacking her certainly will.
But perhaps the motives are mixed. She already knows Zoe and Luther are separated and that Luther still loves his ex (or is it soon-to-be ex?) wife. As well as creating emotional turmoil for Luther, maybe she wants to create a belief in Zoe about her husband's character that will guarantee she will never want to rekindle the relationship.
Either way, Alice is clearly not averse to committing immoral acts to further her own interests. Lying is a lot less bad than the acts she has already committed. So there is no reason to expect her to avoid lying if it turns the screw on Luther.
Lying to further her own objectives is entirely within her character.