As far as I know there's not a direct, contextual link. You have to look at the whole picture of what is said elsewhere in the Bible to come to this conclusion.
And therefore, you don't need to look at other scriptures, which is the point which I have been trying to get across. If all of the information is contained showing that the Lord rained fire and sulfur from the Lord out of heaven. And the context shows that the angel was holding back the destruction until Lot was safe in Zoar, then we don't need to go looking for any underlying interpretation other than what is given.
If scripture says, "The sky is blue, thus sayeth the Lord," then we don't need to go to other scriptures in order to find out what the color blue is or what is meant by the sky. Don't get me wrong! It is good to cross-reference scripture in order to get a clear understanding. But here in this case, everything is contained in the context and there is no need to look at other scriptures to understand the meaning of God raining fire and sulfur down and why he was doing it. Since there is no mention of God using a natural disaster nor the mention of him abandoning or removing his protection from them, then we should not interject it into the scripture. Here is an example taken from those who are Amillennialists:
"And I saw an angel coming down out of heaven, having the key to the Abyss and holding in his hand a great chain.
2He seized the dragon, that ancient serpent, who is the devil, or Satan, and bound him for a thousand years.
3He threw him into the Abyss, and locked and sealed it over him, to keep him from deceiving the nations anymore until the thousand years were ended. After that, he must be set free for a short time."
The Amil, instead of believing what the plain text of the scripture says above, they ignore it and they will site Ps.50:10 and will take the formula there and apply it to the scripture above regarding the thousand years, as follows:
"for every animal of the forest is mine, and the cattle on a thousand hills."
Therefore, since the number of cattle on a thousand hills is an unknown number, they apply the same interpretation to Rev.20:1-7, that is that the thousand years is an unknown number, all the while ignoring the contextual facts that one, there is nothing in the scripture that would lend to the thousand years as not being literal and two, the fact that "a thousand years" is used consistently, being mentioned six times. Here they are doing the same thing that you are doing, which is to ignore the context and interject information that is just not there. Instead of believing the scripture which states that Satan is bound for thousand years, they reject the literal thousand and spiritualize it.
I'm not against you, nor am I just being argumentative, but I am just trying to get you to understand that if the literal sense makes good sense, then don't seek any other sense. That being said, surely God is Almighty and is able to perform the destruction just as the scripture states and that by his will, his power and in his timing and that without the need of natural disasters.