The prophet Lut (May peace be upon him) was leaving his people as Allah ordered him to do:
"The angels said, "O Lot, indeed we are messengers of your Lord; [therefore], they will never reach you. So set out with your family during a portion of the night and let not any among you look back - except your wife; indeed, she will be struck by that which strikes them. Indeed, their appointment is [for] the morning. Is not the morning near?" So when Our command came, We made the highest part [of the city] its lowest and rained upon them stones of layered hard clay, [which were] Marked from your Lord. And Allah 's punishment is not from the wrongdoers [very] far." (Quran 11:81-83)
So, here you can see "and let not any among you look back except your wife; indeed, she will be struck by that which strikes them". The order to not look back was given as the one who had looked back that day may have had the same fate as Lut's (May peace be upon him) Wife.
Lut's (May peace be upon him) Wife was converter into a statue and to prevent the same fate for the Lut (May peace be upon him) and his family this order may had been given.
Allah knows the best