How can you know if the person to whom you lied knows that you lied to her?

Answer:

You are asking the wrong question. You are worried about whether you were caught in a lie. What you really should be concerned about is that liars end up in Hell. "But for the cowardly and unbelieving and abominable and murderers and immoral persons and sorcerers and idolaters and all liars, their part will be in the lake that burns with fire and brimstone, which is the second death" (Revelations 21:8). It doesn't matter whether someone caught you in a lie or not.

The proper thing to do is stop lying and repent of your sins, which would include straightening out the lies that you can and apologizing for them.