Then We saved him and his family, except his wife; she was of the Ghabirin (those who lagged behind).
Allah says, We saved Lut and his family, for only his household believed in him.
Allah said in another Ayah,
فَأَخْرَجْنَا مَن كَانَ فِيهَا مِنَ الْمُوْمِنِينَ
فَمَا وَجَدْنَا فِيهَا غَيْرَ بَيْتٍ مِّنَ الْمُسْلِمِينَ
So We brought out from therein the believers. But We found not there any household of the Muslims except one (of Lut and his daughters). (51;35-36)
Only his wife (from his family) did not believe, remaining on the religion of her people. She used to conspire with them against Lut and inform them of who came to visit him, using certain signals that they agreed on. This is why when Lut was commanded to leave by night with his family, he was ordered not to inform his wife or take her with him.
Some said that she followed them, and when the torment struck her people, she looked back and suffered the same punishment as them.
However, it appears that she did not leave the town and that Lut did not tell her that they would depart. So she remained with her people, as apparent from Allah's statement,
إِلاَّ امْرَأَتَهُ كَانَتْ مِنَ الْغَابِرِينَ
except his wife; she was of the Ghabirin.
meaning, of those who remained, or they say;of those who were destroyed, and this is the more obvious explanation.