( فَأَنجَيْنَاهُ) (So We saved him): A miracle happened but in this verse Allah (swt) does not explicit what it was. The phrase: (So We saved him) means that a punishment surely had befallen those people so that Allah (swt) saved Prophet Lot (PBUH) from it.

( إِلَّا امْرَأَتَهُ كَانَتْ مِنَ الْغَابِرِينَ) (except for his wife; she was of those who remained [with the evildoers]): His wife remained in her place together with the rest who remained in their homes, so that she too tasted the grave punishment that had befallen upon her people.

Allah (swt) says:

 ضَرَبَ اللَّهُ مَثَلًا لِّلَّذِينَ كَفَرُوا امْرَأَتَ نُوحٍ وَامْرَأَتَ لُوطٍ ۖ كَانَتَا تَحْتَ عَبْدَيْنِ مِنْ عِبَادِنَا صَالِحَيْنِ فَخَانَتَاهُمَا فَلَمْ يُغْنِيَا عَنْهُمَا مِنَ اللَّهِ شَيْئًا وَقِيلَ ادْخُلَا النَّارَ مَعَ الدَّاخِلِينَ

(Allah presents an example of those who disbelieved: the wife of Noah and the wife of Lot. They were under two of Our righteous servants but betrayed them, so those prophets did not avail them from Allah at all, and it was said, “Enter the Fire with those who enter.”) (At-Tahrim: 10)

This is a declaration that faith is exclusively a matter of choice. No person on the face of the planet can be forced to believe or to disbelieve. As a proof of that, we have the example of the wives of Prophets Lut (PBUH) and Noah (PBUH). Both these women were wives of Prophets, yet they did not believe. Prophet Noah’s (PBUH) wife drowned, and Prophet Lut’s (PBUH) wife died under the stones and the turning over of the whole village. On the contrary, the wife of the Pharoh, who claimed himself to be a god, was a believer:

  وَضَرَبَ اللَّهُ مَثَلًا لِّلَّذِينَ آمَنُوا امْرَأَتَ فِرْعَوْنَ إِذْ قَالَتْ رَبِّ ابْنِ لِي عِندَكَ بَيْتًا فِي الْجَنَّةِ وَنَجِّنِي مِن فِرْعَوْنَ وَعَمَلِهِ وَنَجِّنِي مِنَ الْقَوْمِ الظَّالِمِينَ

(And Allah presents an example of those who believed: the wife of Pharaoh, when she said, “My Lord, build for me near You a house in Paradise and save me from Pharaoh and his deeds and save me from the wrongdoing people.”) (At-Tahrim: 11)