Generally, doors in the Bible represent the initial desires for good and concepts of truth that introduce us to new levels of love and understanding, and even to the Lord Himself. Since a “house” represents a person’s desires, affections and passions, the door serves to introduce true ideas that can put those desires into action.

In John 10:7, the door signifies the Lord, who is good itself and truth itself. (Arcana Coelestia 2356[2])

In Revelation 3:8; 4:1, the door signifies admission to the arcana of heaven revealed. (Apocalypse Explained 260[2])

The meaning depends on context, of course. For example, references to doorposts and lintels are making a distinction between introductory goods and introductory truths. And, in Sodom, Lot's house had two doors -- an inner one and an outer one. When, in Genesis 19:6, Lot tried to convince the men of Sodom not to attack the angels visiting him, he went outside the inner door, but stayed inside the outer door. There, the outer door represents a desire for good that is resistant to the falsity represented by the men of Sodom; the inner door represents true ideas springing from that desire for good. Someone nurturing a desire for good could be admitted through the first door, but would have to learn the truth about how to express that desire before being admitted through the second.

(Odkazy: Genesis 19)

2356. That 'Lot went out to them to the door (janua)' means that he acted cautiously is clear from the interior sense of 'the door' and of 'going out to the door'. 'A door' in the Word means that which introduces or leads the way either towards truth, or towards good, or towards the Lord. Consequently 'a door' in addition means truth itself, also good itself, as well as the Lord Himself, for truth leads to good, and good leads to the Lord. Such things were represented by the door and the veils of the Tent of Meeting, and also of the Temple, see 2145, 2152, 2576.

[2] That this is the meaning of 'a door' is evident from the Lord's words in John,

He who does not enter by the door into the sheepfold but climbs in by another way, that man is a thief and a robber. But he who enters by the door is the shepherd of the sheep. To him the doorkeeper opens. I am the door of the sheep; if anyone enters through Me he will be saved. John 10:1-3, 7, 9.

Here 'door' stands for truth and good, and so for the Lord who is truth itself and good itself. This shows what is meant by being let in through the door into heaven, and therefore what is meant by 'the keys' which unlock it.

[3] Here however 'a door' means a particular type of good that was suited to the disposition of those who besieged the house, for a distinction is made here between 'a door' (janua) and 'a door' (ostium). The former was on the outside of the house, as is evident from the fact that Lot went out and closed the door (ostium) behind him. This type of good was blessedness of life, as is clear from what follows shortly where he persuaded those who were immersed in falsity and evil. For such people do not allow themselves to be persuaded by actual good itself; indeed they reject it. From these considerations it is evident that here 'going out to the door' means that he acted cautiously.