Scripture just says she looked back.
Gen 19:25 And he overthrew those cities, and all the plain, and all the inhabitants of the cities, and that which grew upon the ground.
Gen 19:26 But his wife looked back from behind him, and she became a pillar of salt.
Being killed for mourning doesn't make sense but looking back because she liked the sinful life she had there does.
A second issue is that scripture says Lot had two daughters and two daughters came with him so there is no daughters to mourn for anyways.
In my studies of the writings of Moses, I have found that he has great skill with regard to brevity, saying a lot with a few words.
Take a look at this section here for example.
12 Then the two men said to Lot, “Whom else do you have here? A son-in-law and your sons and daughters, and whomever you have in the city, bring them out of the place; 13 for we are about to destroy this place, because their outcry has become so great before the Lord that the Lord has sent us to destroy it.” 14 So Lot went out and spoke to his sons-in-law, who were to marry his daughters, and said, “Up, get out of this place, for the Lord is destroying the city.” But he appeared to his sons-in-law to be joking.
15 When morning dawned, the angels urged Lot, saying, “Up, take your wife and your two daughters who are here, or you will be swept away in the punishment of the city.”
Not only did Lot have two daughters living at home with him, according to verse 12, he also had a son-in-law living at home with him. I believe Moses intends to imply that not only did Lot's household consist of two unmarried daughters, but it also consisted of a married couple: a son-in-law and his betrothed. According to verse 15, Lot had two daughters "who are here." And according to verse 12, Lot also had a son-in-law who "you have here." In other words, living with Lot and his wife were two unmarried daughters and a married couple. So Lot had three daughters living at home, two unmarried daughters, and one married daughter.
He also had relations living elsewhere in the city just as the Angel said, "whomever you have in the city." Lot had other sons-in-law and he went to them to convince them to leave the city. His sons-in-law thought he was just kidding. Bear in mind that each son-in-law was engaged to be married to one of Lot's daughters. Moses refers to them as "sons-in-law" because the couple lived together as an engaged couple (just as Jesus' parents did.)
In other words, Lot had more than two daughters, he had many, some living in his household and others living with sons-in-law. Lot's engaged daughters would remain with the sons-in-law.
With regard to Lot's wife, Moses writes,
18 But Lot said to them, “Oh no, my lords! 19 Now behold, your servant has found favor in your sight, and you have magnified your compassion, which you have shown me by saving my life; but I cannot escape to the mountains, for the disaster will overtake me and I will die; 20 now behold, this town is near enough to flee to, and it is small. Please, let me escape there (is it not small?) so that my life may be saved.” 21 And he said to him, “Behold, I grant you this request also, not to overthrow the town of which you have spoken. 22 Hurry, escape there, for I cannot do anything until you arrive there.” Therefore the town was named Zoar.
23 The sun had risen over the earth when Lot came to Zoar. 24 Then the Lord rained brimstone and fire on Sodom and Gomorrah from the Lord out of heaven, 25 and He overthrew those cities, and all the surrounding area, and all the inhabitants of the cities, and what grew on the ground. 26 But Lot’s wife, from behind him, looked back, and she became a pillar of salt.
During the escape, Lot begged the Angels to allow him and his family to enter Zoar for protection. Moses tells us in verse 23 that Lot came to Zoar. Moses tells us in verse 26 that Lot's wife looked back "from behind him." What does he mean?
Here is the picture I get. Lot and his family are headed for the mountains for protection. Lot realizes that in his old age and with his wife and daughters, he is afraid that they won't make it to the mountains in time. So lot asks the Angel if the town of Zoar would suffice. Moses tells us in verse 23 that Lot successfully arrived at Zoar at sunrise. In verse 26 Moses says that Lot's wife was "behind him" meaning that she was still in transit; she hadn't yet arrived in Zoar. She fell behind and therefore she was still in the blast zone (so to speak.) She stopped to look back, which is why she lagged behind Lot.
Does that make sense?