Lot was a problem from the very beginning. Abraham should have been obedient and left Lot behind, but true to form, he disobeyed (Gen. 12:1-4). It wasn't long before Abraham would discover that Lot was bad news. Lot showed his lack of respect for Abraham by allowing his herdsmen to quarrel with those of his benefactor. When given the opportunity, instead of choosing an inferior place for his flock so that Abraham could have the best place, he showed his character by his choice (Gen. 13:5-12). He showed his lack of wisdom in choosing a place filled with wicked sinners (Gen. 13:13). He apparently fit right in because he rose to a position of authority in Sodom as one who sat in the gate (cp. Gen. 19:1 w/ Deut. 21:19-21).
Later, when Lot was taken captive, Abraham risked his life to rescue him (Gen. 14:12-16). Lot went right back to Sodom, a decision that would ultimately result in his offering his daughters to a large mob of homosexuals to prevent them from attacking his "guests" (Gen. 19:4-8). He soon discovered that those same daughters, obviously now widows with little respect for their dad, bore his children (Gen. 19:14, 30-38). Lot's offspring finally end up living in Moab and it is not clear whether or not they ever entered the Promised Land (Deut. 2:9). Psalm 83:8 tells us Lot's descendants were closely tied to the enemies of Israel.
Abraham's problems brought on by failing to leave Lot behind, Lot's continuing to dwell among the enemies of God, and his disaster of a family, did not alter the fact that Lot was a man of God. Apparently he was in the world, but not of the world. 2 Peter 2:7-8 reveals that Lot was a just or righteous man, and that he was troubled deeply by the sin that surrounded he and his family. Just as Noah and Abraham were considered righteous because they accepted the gift of faith they received, fearing and believing God, Lot had to have responded to the grace of God in order to be declared righteous (see the entire first paragraph of yesterday's post).
The main reason that I see Lot as a picture of the Church is because God does. Both Noah and Lot are presented as examples of people who, though certainly unworthy, were lifted up above the destruction of the wrath of God below. Jesus used Lot and Noah to describe the suddenness of the mystery of the Rapture and the Tribulation to follow (Matt. 24:36-39; Lk. 17:25-30; 1 Cor. 15:51-57; 1 Thes. 4:13-18). Noah and Lot were sinners saved by the grace of God. They committed awful sin following their coming to understand God's willingness to save them. They were not worthy to escape and neither is the Church. But, praise God, His Word assures His children that we are not to fear the future, but to look forward to it in the comfort of hope (Titus 2:13). Maranatha! Come Lord Jesus!