The solution is quite simple. You merely have to stop reading the text like a Jehovah's Witness.
For JWs, the Biblical texts are the complete stories that make up a compendium of religious doctrine. For my people, the Jews who composed them, these stories have been compacted for the purpose of liturgical reading, to hit only the highlights of the stories that come from our history and tradition. We did not write them to be read out of context with these things, but the Witnesses ignore them all and attempt to read the text as if it was a journalistic news report on the past and that there is nothing more to them.
Every year in the Jewish month of Heshvan, the historical anniversary of these events is marked by the reading of Parashat Vayiera, the name of this section of the Law of Moses, namely Genesis 18:1-22:24 in the synagogue. Designed specifically for this, the written story only hits the highlights so that the religious lessons can be drawn out.
What the written text doesn't explain is the Jewish understanding that Lot's wife was from Sodom. While Lot was welcoming of strangers in the tradition of his family (in imitation of Abraham), Lot's wife was like the rest of her people. Part of the wife's lack of hospitality is seen in the Torah reading itself in that the dinner she helps to prepare for the guests is far more modest. (Genesis 18:6-8 with 19:3.) This is but a reflection of her siding with her people that is understood by the Jewish audience, part of a plot to rape and even murder the visitors if need be.
Instead of reading Vayeira as a story about homosexuality, the Jews see the sin of Sodom and Gomorrah as the violent inhospitable acts the towns were known for perpetrating upon travelers. Lot's wife was instrumental to the townspeople learning that Lot was welcoming strangers into their midst, with one tradition saying that Lot's wife used the preparation of the pathetic dinner as a reason to beg salt from the neighbors with the real intention of spreading the news of her husband's visitors and thus setting the attack in motion.
When her town was destroyed, Lot's wife turned around from the shielding protection of the angel and chose to weep over its demise instead of flee. So she was "turned into salt" as a "fitting" punishment for the attempted murder (and her previous actions of similar acts upon strangers with her people).
You might say the story of Lot's wife is comparable with David's sin. Both were involved in murder plots, David was involved in adultery, Lot's wife helped to orchestrate group rapes and the murder of visitors to Sodom, both lost family members due to their sin, and both were offered mercy from God. Whereas David accepted God's mercy, Lot's wife refused it and received a due punishment.
The texts were not designed to be read out of context with their place in the liturgical calendar. Even Christians with the Revised Common Lectionary follow a similar annual cycle of Sunday readings. Jehovah's Witnesses have no liturgy, and no one from Watchtower land even knows what a liturgical calendar is. Ignorant of this, the JWs read the Bible disconnected with the cultural background and understanding that comes with it. When you do this, the stories cannot be reconciled as they are not as complete as the Witnesses claim they are.