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.
Dear sister, it is a great blessing that a person is enabled to become steadfast on the right path and on the obedience of his/her Lord, especially at this time and age where afflictions are widespread. So, you should be grateful to Allaah for this by treading the path of staying firm on Allaah’s religion, by seeking beneficial knowledge and performing good deeds as much as possible and keeping company with righteous Muslim women.
There is no doubt that lying is forbidden and is a great major sin and it is not permissible for a Muslim to resort to it unless in case of necessity that cannot be repelled expect by lying, or for a preponderant benefit. For more benefit, please refer to Fatwa 88412.
What we can say here is that since this matter has not taken place yet, then it is more appropriate for you to leave that country and move to your country or migrate to any other country where you would feel safe and reserve your religion and avoid such embarrassment.
If it is not possible for you to migrate from that country and you can refrain from travelling in order to avoid this embarrassment, then do not travel. With regard to getting in touch with the family and others, then this has become easy at this time and age thanks to the availability of the audio and video means of communication.
In case there is urgent necessity to travel for a given reason, then you may answer the question (Have you ever lied to authorities?) with something that is not considered a lie, like saying ‘no’ while intending that you did not lie to them after you repented.
Allaah Knows best.