Both Noach and Lot survive an instance of large scale destruction at the hand of God, with special Divine Providence saving them. Noach via the ark, Lot through leaving the city and also by staying in Tzoar.
But then, at the end of Bereshit 19:
Compare/contrast to Noach, upon leaving the ark (in Bereshit 9), who became drunk, and whose children (at least two of them) covered their father's nakedness:
Also, contrast Noach's awareness of what happened, after recovering from his drunkenness, with Lot's obliviousness. By Noach:
While by Lot:
|א וַיְבָרֶךְ אֱלֹקִים, אֶת-נֹחַ וְאֶת-בָּנָיו; וַיֹּאמֶר לָהֶם פְּרוּ וּרְבוּ, וּמִלְאוּ אֶת-הָאָרֶץ.||1 And God blessed Noah and his sons, and said unto them: 'Be fruitful and multiply, and replenish the earth.|
Nothing deep to say here. Rather, I just spotted this potential connection.