Lut is ordered to leave with His Family during the Night
Allah tells us that His angels ordered Lut to set out after part of the night had passed. They told him to walk behind them, to protect them. Similarly, the Messenger of Allah ﷺ would walk in the rear of the army on military campaigns, in order to help the weak and carry those who had no means of transport.
وَلاَ يَلْتَفِتْ مِنكُمْ أَحَدٌ
(and let no one amongst you look back,) meaning - when you hear the people screaming from their torment, do not turn around to look at them; leave them to face whatever punishment and vengeance is coming to them.
وَامْضُواْ حَيْثُ تُؤْمَرُونَ
(but go on to where you are ordered.) - it is as if they had a guide with them to show them the way.
وَقَضَيْنَآ إِلَيْهِ ذَلِكَ الاٌّمْرَ
(And We made this decree known to him) meaning - We already told him about that.
أَنَّ دَابِرَ هَـؤُلآْءِ مَقْطُوعٌ مُّصْبِحِينَ
(that those (sinners) would be rooted out in the early morning.) meaning in the morning, as in another Ayah:
إِنَّ مَوْعِدَهُمُ الصُّبْحُ أَلَيْسَ الصُّبْحُ بِقَرِيبٍ
(Indeed, morning is their appointed time. Is not the morning near) 11:81