Christ is speaking to his disciples warning about the time when the Antichrist will show up, and he says "remember Lot's wife".
Luke 17:31-32- In that day, he which shall be upon the housetop, and his stuff in the house, let him not come down to take it away: and he that is in the field, let him likewise not return back. Remember Lot's wife.
This retelling in Matthew doesn't mention fleeing. In Matthew's version it's talking about the coming of the Son of Man. Matthew gives his memoirs through the lens of the King of the Jews and focuses on Christ's being the king.
Matthew 24:30- And then shall appear the sign of the Son of man in heaven: and then shall all the tribes of the earth mourn, and they shall see the Son of man coming in the clouds of heaven with power and great glory.
Luke, however, focuses on Christ being the Son of man, or human. And in his version he is focusing on Christ's mortality.
Luke 17:25- But first must he suffer many things, and be rejected of this generation.
Christ is warning that He didn't come to set up His earthly kingdom at that time, He came to die for the sins of the world. But the disciples just couldn't grasp that concept.
The memoir that Luke gives of this story is that the Jews are told to flee away from the coming destruction that will rain down on the world during the time of the Tribulation.
If we look at the story of Lot, we will see what Christ is warning about.
God had visited Abram and explained that He was going down to Sodom to see if the wickedness that He was hearing in heaven was as great as it seemed. Abram had gotten God to agree to sparing the entire wicked city if there were just ten righteous people in it.
Now, we know that Lot and his wife and two of his daughters were in the city, along with at least two other married daughters. So Abraham supposed there were at least 6 righteous in Lot's family, possibly 8 if the two married daughters were with righteous men. That would leave only 2 people that would need to be righteous for the city to be spared.
Unfortunately, it is far more likely that corruption happens. The two daughters didn't marry good men, and because of that they were corrupted and not considered to be righteous.
Genesis 19:14- And Lot went out, and spake unto his sons in law, which married his daughters, and said, Up, get you out of this place; for the LORD will destroy this city. But he seemed as one that mocked unto his sons in law.
Lot was physically removed from the city by the angels.
Genesis 19:15-17- And when the morning arose, then the angels hastened Lot, saying, Arise, take thy wife, and thy two daughters, which are here; lest thou be consumed in the iniquity of the city. And while he lingered, the men laid hold upon his hand, and upon the hand of his wife, and upon the hand of his two daughters; the LORD being merciful unto him: and they brought him forth, and set him without the city. And it came to pass, when they had brought them forth abroad, that he said, Escape for thy life; look not behind thee, neither stay thou in all the plain; escape to the mountain, lest thou be consumed.
Lot had moved in with these sinners and now he was finding it hard to leave. Who wouldn't? His daughters were there. His possessions were there. His business was there.
We won't go into details about how low he sank while he was there. Suffice it to say that he lost at least two daughters when the judgment fell, and ended up a single dad with two daughters who didn't exactly make very wise choices (all because of the influence of the wicked city on his family).
II Peter 2:7-8- And delivered just Lot, vexed with the filthy conversation of the wicked: (For that righteous man dwelling among them, in seeing and hearing, vexed his righteous soul from day to day with their unlawful deeds;)
But, that wasn't where he should stay if he wanted to flee from the wrath to come. In Lot's day, the Lord was merciful and removed him before the judgment fell.
Genesis 19:24-26- Then the LORD rained upon Sodom and upon Gomorrah brimstone and fire from the LORD out of heaven; And he overthrew those cities, and all the plain, and all the inhabitants of the cities, and that which grew upon the ground. But his wife looked back from behind him, and she became a pillar of salt.
They were outside the destruction zone, and yet when his wife looked back to all that she lost she was struck by the judgment.
In the future, the people are warned to flee from the wrath to come, but if they don't fun they will end up suffering when it falls!
Revelation 18:4- And I heard another voice from heaven, saying, Come out of her, my people, that ye be not partakers of her sins, and that ye receive not of her plagues.
God tells the people to flee and hide when the Antichrist goes into the rebuilt temple and sits on the ark of the covenant and proclaims himself to be god.
Matthew 24:15-21- When ye therefore shall see the abomination of desolation, spoken of by Daniel the prophet, stand in the holy place, (whoso readeth, let him understand:) Then let them which be in Judaea flee into the mountains: Let him which is on the housetop not come down to take any thing out of his house: Neither let him which is in the field return back to take his clothes. And woe unto them that are with child, and to them that give suck in those days! But pray ye that your flight be not in the winter, neither on the sabbath day: For then shall be great tribulation, such as was not since the beginning of the world to this time, no, nor ever shall be.
It's going to be an awful time. Many will die. Many will suffer bereavement. And many more will accept the mark of the beast and lose their soul.
Heed the warning that was given. Don't try to gather things up or save your possessions. He isn't just talking about the salvation of your physical life, He's warning about the possible damnation of your eternal soul. Run and don't look back!
Don't think for a minute that God will withhold his righteous judgment because you don't want to obey.