The angels not only pulled Lot into the house, but they also will later grabbed Lot and his family by the hand and pulled them out of a city that was going to be consumed by fire, too. This reminds me of the passage in Jude.
For Jude 1:23 says,
"And others save with fear, pulling them out of the fire; hating even the garment spotted by the flesh"
Today, believers preach the consequences of not following God (Which is destruction in the Lake of Fire). In by doing so, they are literally pulling men's souls out of the fire.
Also, in Lot's Story here in Sodom: The fact that the door was shut to these sinful men shows that they were being separated. We see a parallel of this in the Parable of the Ten Virgins. The wise virgins who had enough oil in their lamps were able to make it to the wedding on time and the door was shut behind them. But the foolish virgins did not have enough oil did not get there on time and they knocked on the door and were not able to enter. They were shut out. The foolish and sinful people of this world are shut out of God's secret place for those who are faithful to Him.