All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Calling to Allaah, enjoining good and forbidding evil are among the communal (Fardh Kifaayah) obligations of a Muslim and they would not become an individual (Fardh ‘Ayn) obligation on you unless there is no one else to carry them out.
Besides, it is an obligation to seek the permission of the parents in regard to performing the communal obligations including Jihaad (fighting in the Cause of Allaah), so it is not permissible for you to go out for D’awah except with their permission. For more benefit, please refer to Fatwa 81971.
On the other hand, lying is forbidden and a great major sin, so it is not permissible for you to lie and it is even a greater sin to lie to your parents as this involves cutting ties with them. For more benefit, please refer to Fatwa 88412.
However, a Muslim may carry out Da’wah within his surrounding area according to his ability and he should cooperate with some righteous people in his mosque and the mosques near his house in calling people to Allaah and spreading goodness to them.
May Allaah increase your keenness to do good deeds and help you to perform acts of obedience and to call people to Him.
For more benefit, please refer to Fataawa 85419 and 87749.
Allaah Knows best.