Hi Alpha03, after re-reading your post, I think your complaint here may be about the principle of things, rather than the actual events. Perhaps it is not "what" your sister lied about, but it is "the pattern of dishonesty" that troubles you. Even if the things she lied about seems minor on the surface, you do not like to be in a relationship where you are being constantly lied to (?)

Being that she is a family member, I know you can't completely avoid her. But asking to borrow things from her and initiating contact with her would only make things worse.

I hope you find peace