If I was to look at purgatory from the view of C. S. Lewis's The Great Divirce- I would say yes, because I think the lake of fire is the bringing of every hidden thing to light, as light is fire to darkness. The answer to chaos(without form and void) is "Let there be light". The light shines in the darkness and the darkness cannot overcome it. Classic Catholic purgatory where you can pray people out of it or make offerings to get them out, I can't see that.
2 Cor 4: 3 But even if our gospel is veiled, it is veiled to those who are perishing, 4 whose minds the god of this age has blinded, who do not believe, lest the light of the gospel of the glory of Christ, who is the image of God, should shine on them. 5 For we do not preach ourselves, but Christ Jesus the Lord, and ourselves your bondservants for Jesus' sake. 6 For it is the God who commanded light to shine out of darkness, who has shone in our hearts to give the light of the knowledge of the glory of God in the face of Jesus Christ.
So I think that "tormented(corrected) in the presence of the Lamb and His holy angels"(Rev 14:12) means that in the presence of all the witnesses of all the ages, the righteousness of Christ crucified will "tear down every stronghold and fortress that exalts itself against the true knoweldge of God" until "every knee has bowed whther in heaven or one earth or under the earth, and every tongue confess that Jesus Christ is Lord to the glory of God the Father" which will subject every adversary that remains after this age and the next, including those whose names are not written in the Lamb' book of life.
The wicked are not in the presence of God to be corrected in this life.
"If anyone worships the beast and his image, and receives his mark on his forehead or on his hand, 10 he himself shall also drink of the wine of the wrath of God, which is poured out full strength into the cup of His indignation. He shall be tormented with fire and brimstone in the presence of the holy angels and in the presence of the Lamb. (Rev 14)
Noticing that the correction for a wayward saint was to "Take them before the whole assembly".... I think aionian correction will be the same in essence- thats what I believe the lake of fire is, a kind of forced intervention before the whole family of God.
22 But you have come to Mount Zion and to the city of the living God, the heavenly Jerusalem, to an innumerable company of angels, 23 to the general assembly and church of the firstborn who are registered in heaven, to God the Judge of all, to the spirits of just men made perfect, 24 to Jesus the Mediator of the new covenant(the bold part is the lake of fire imo), and to the blood of sprinkling that speaks better things than that of Abel.
25 See that you do not refuse Him who speaks. For if they did not escape who refused Him who spoke on earth, much more shall we not escape if we turn away from Him who speaks from heaven, 26 whose voice then shook the earth; but now He has promised, saying, "Yet once more I shake not only the earth, but also heaven." 27 Now this, "Yet once more," indicates the removal of those things that are being shaken, as of things that are made, that the things which cannot be shaken may remain.
28 Therefore, since we are receiving a kingdom which cannot be shaken, let us have grace, by which we may serve God acceptably with reverence and godly fear. 29 For our God is a consuming fire.
I think this applies to Hebrews 12, a picture of heavenly Zion(upon this mountain I will remove the covering(vail KJV) that covers the peoples, Isaiah) and the heavenly assembly, interestingly concluding with not escaping because, "our God is a consuming fire"