Is it obligatory for my sister to make up the prayers she missed previously, or should I wait until she becomes regular in her prayers before telling her about making them up?

Your sister must repent to Allah the Almighty for her negligence in prayer and make up for what she has missed. She must commit to her prayers for the remainder of her life, because there is disagreement about the disbelief of one who abandons prayer. You must admonish her and warn her of Allah's punishment, and encourage her with what Allah has prepared if she repents and safeguards His obligations.