In Islam, Taqiya or Taqiyya (تقیة taqiyyah, literally "prudence, fear") is a precautionary dissimulation or denial of religious belief and practice in the face of persecution. Another term for this concept, kitmān (lit. "action of covering, dissimulation"), has a more specific meaning of dissimulation by silence or omission.This practice is emphasized in Shia Islam whereby adherents are permitted to conceal their religion when under threat of persecution or compulsion.
Thank you for your question. It is necessary for a person to protect their life and so there would be no punishment for lying in the situation described.
May you always be successful
Taqiyyah has conditions and it aims to save the believers, but when mam Husain (AS) faced a complete different situation when the whole religion was in danger and here was no way at all to save Islam but to give his life to save Islam. There was no question of Taqiyyah in such dangerous situation. Neither Imam Ali (AS) nor any other Imam faced such situation, and if any Infallible faces such situation, they will definitely do exactly what Imam Husain (AS) did in sacrificing their lives to save Islam.
If Taqqyah is really required in your circumstances, then yes. It
means that if you don’t fold your arms during prayer with your Sunni
family members, it can cause you real risk and harm.
So Taqayyah will be applicable to avoid such expected harm. It is good
to inform your Sunni family members that folding arms is not in the
Salaah of the many Sunnis who are followers of the Maaliki sect. So
many millions of Maaliki Sunnis do not fold their arms during Salaah.
This is the practice of the Maaliki Sunnis. But if you want to search
the evidence of folding hands during Salaah ,you will never find an
authentic Hadith that te Holy Prophet (SAWA) folded hands during
Salaah. Folding hands during Salaah was ordered by Umar ibn Khattab
during his government time. None of the leading Sunni scholars could
claim that folding hands during Salaah is obligatory.
Leading Sunni scholar Sheikh Sayyed Sabiq in his book Fiqh al Sunnah
stated that there is not a single authentic Hadith suggesting that the
Holy Prophet (SAWA) folded his hands during even one Salaah