I don't know, I never thought about that one before. But looking at what you posted I see that the Lord had to drag them out of the city. Once out of the city God let them go to walk on their own. Mrs. Lot looked back and turned to salt.
That looks to me like a picture of salvation with God dragging them out, and then their walk afterwards being a type of the Christian walk after salvation. Some people move forward in their walk and some desire to go back. However we know that people are not allowed to go back and at times the Lord will take a child home instead of letting them stay here and wallow in their sins.
You might also want to consider the (angel/God motivated ?) offer to Lot's sons-in law (and their response).
Another Genesis salvation picture to consider is Noah ... the ark ... the flood.
I don't believe that the text says that God forced Noah (or any member of his family) to board the ark.
It appears that they all chose to obey God, ... while all those which perished chose to disobey.
Becky