The Searcher..
This is a helpful commentary from Barnes :
Suffering the vengeance of eternal fire - The word rendered “suffering” ( ὑπέχουσαι hupechousai) means, properly, “holding under” - as, for example, the hand; then to hold toward any one, as the ear - to give attention; then it is used as denoting to hold a discourse toward or with any one, or to hold satisfaction to any one, to make atonement; and then as “undergoing, paying, or suffering punishment,” when united, as it is here, with the word δίκην dikēn(punishment, or vengeance). See “Rob. Lex.” Here it expresses the idea of undergoing punishment. The word properly agrees in the construction with “cities,” ( πόλεις poleisreferring to Sodom and Gomorrah, and the cities around them; but the things affirmed relate to the “inhabitants” of those cities. The word “vengeance” means punishment; that is, such vengeance as the Lord takes on the guilty; not vengeance for the gratification of private and personal feeling, but like that which a magistrate appoints for the maintenance of the laws; such as justice demands. The phrase “eternal fire” is one that is often used to denote future punishment - as expressing the severity and intensity of the suffering. See the notes, Matthew 25:41 . As here used, it cannot mean that the fires which consumed Sodom and Gomorrah were literally eternal, or were kept always burning, for that was not true. The expression seems to denote, in this connection, two things:
(1)That the destruction of the cities of the plain, with their inhabitants, was as entire and perpetual as if the fires had been always burning - the consumption was absolute and enduring - the sinners were wholly cut off, and the cities forever rendered desolate; and,
(2)that, in its nature and duration, this was a striking emblem of the destruction which will come upon the ungodly. I do not see that the apostle here means to affirm that those particular sinners who dwelt in Sodom would be punished forever, for his expressions do not directly affirm that, and his argument does not demand it; but still the “image” in his mind, in the destruction of those cities, was clearly that of the utter desolation and ruin of which this was the emblem; of the perpetual destruction of the wicked, like that of the cities of the plain. If this had not been the case, there was no reason why he should have used the word “eternal” - meaning here “perpetual” - since, if in his mind there was no image of future punishment, all that the argument would have demanded was the simple statement that they were cut off by fire.
The passage, then, cannot be used to prove that the particular dwellers in Sodom will be punished forever - whatever may be the truth on that point; but that there is a place of eternal punishment, of which that was a striking emblem. The meaning is, that the case was one which furnished a demonstration of the fact that God will punish sin; that this was an example of the punishment which God sometimes inflicts on sinners in this world, and a type of that eternal punishment which will be inflicted in the next.