Okay, I had my own share of pain in dealing with a toxic female relative so I want to be compassionate. I get that you are upset about her dishonesty, as you answered Sarah. Just a couple of things I'm struggling to understand:

Why are you the one to initiate contact with her, by asking to borrow things, approaching her at the wedding, etc.?

I would not want to borrow anything from my toxic relative because that would just tie me to her all the more.

And I wish my toxic relative would ignore me at functions and leave me alone (that would be a dream come true).

It sounds like you are pursuing a relationship with your sister (asking to borrow things, not wanting to be ignored by her) and you are upset that you cannot have this. But why do you want to have a relationship with a dishonest, toxic person? You deserve a better life; to live in peace without constant interactions with someone like that.