She was not a believer. This is all that Quran tells us. She preferred her people to Lot and his message, but we do not know if she supported or agreed with their homosexuality, too. Her sin is described as:
ضَرَبَ اللّٰہُ مَثَلًا لِّلَّذِیۡنَ کَفَرُوا امۡرَاَتَ نُوۡحٍ وَّ امۡرَاَتَ لُوۡطٍ ؕ کَانَتَا تَحۡتَ عَبۡدَیۡنِ مِنۡ عِبَادِنَا صَالِحَیۡنِ فَخَانَتٰہُمَا فَلَمۡ یُغۡنِیَا عَنۡہُمَا مِنَ اللّٰہِ شَیۡئًا وَّ قِیۡلَ ادۡخُلَا النَّارَ مَعَ الدّٰخِلِیۡنَ
[They should know that that each person is responsible for his deeds.] God cites the example of Noah’s wife and Lot’s wife for the disbelievers. Both were married to two righteous ones from among Our servants, but they betrayed their husbands.[47] So, their husbands could in no way protect them from God, and both women were ordered: “Go, enter the Fire with those who enter it.” (66:10)
This refers to their betrayal in the matter of religion. The actual word used is: خَانَتَا. It does not necessarily relate to marital betrayal so that the wives be regarded as guilty of adultery.