How can one deal with a younger sister who does not pray, frequently lies, and quarrels, and whose actions have caused all family members to complain?

You should turn to Allah, seeking guidance for her, and deal with her as a person who understands her own best interests. She should be connected with righteous girls, and cautiously distanced from bad company. Show her joy for the good deeds she does and offer her gifts. She can be advised through someone she loves, and admonitions can be delivered indirectly. She must be advised and encouraged to pray through both encouragement and deterrence, and through both gentleness and firmness, even if it sometimes requires using severity for her own benefit.