1) Neither is correct. The action took place in the past, so what do you think the correct word should be?
2) Omitting 'had' would change the tense to the present.
Please note that a better title would have been I don't know why she lie/lies to you this afternoon.
Extract from the Posting Guidelines:
'Thread titles should include all or part of the word/phrase being discussed.'
Additionally, there is no need for greetings, and 'Mdm' is an unacceptable abbreviation.
Interested in Language