Abrother,
Let me tell you first of all as a father and a brother I can understand your confusion as to how to handle the situation.
You say your family knows, and you say your sister is known to lie. This however is not much information to work with.
I would have to ask some questions for more details in order to make an educated suggestion.
What is the relationship between your mother, your father, your sister and you? Are you all under one roof? Is there anything that your sister could be seeking revenge for? Does your father watch films or read books with pornographic material? Does your sister live at home? Have you spoken to your father about your fears? Does your father drink alcohol?
What it all sums up to is what is the relationship in your home?
What does your sister mean about he used to, when did he stop?
And think long and hard, is there a promise that wasn’t kept, an argument that led up to the accusation being made? Or are you perhaps a family that is broken and wounded by a deserting father, and he shows little care or love for his angry wounded children?
My young friend I would tell you most of all that God loves you, and He knows just what you need for peace of mind. You must understand that no man is perfect and no father is without sin. God however is our sin free Father in Heaven, and He is more then willing to pull you up to His chest in a warm comforting hug if you will allow Him to.
The only thing that any of us can do is write words with hopes that they comfort you in one way or another, and offer uneducated advice. God on the other hand knows all things, He knows all truth, and He knows the words you need to hear. Pray that if your sister is lying that He will convict her heart and she will repent both to your father and to your heavenly Father. If your father is guilty pray that God will convict his heart and he will seek forgiveness from you his family and from God. And pray that God will give you and your family the strength and the wisdom you need to deal with the situation no matter how it turns out.
Until then, all of us will be praying for you.
Your Brother in Christ, Jerry-The Berlin Bear