We seem to be in agreement. Fire should be seen as purifying.Personally, I think heaven and hell are states of mind and the difference is service to all as self vs service solely to self and disparity towards other selves.
Jesus said, "He who wishes to be greatest, must be servant to all."
As you noted, the richman consistently thought of "himself", "his" family, "his" vs others. The division between him and abraham and lazarus was created by himself in making the difference.
The lake of fire is a purifying scenario; which removes the attachments of the earthly experience. Can be related to the same situation expressed in Zechariah 13:9
And I will put this third into the fire, and refine them as one refines silver, and test them as gold is tested. They will call upon my name, and I will answer them. I will say, ‘They are my people’; and they will say, ‘The LORD is my God.’
and again
malachi 3:3
And he shall sit as a refiner and purifier of silver: and he shall purify the sons of Levi, and purge them as gold and silver, that they may offer unto the Lord an offering in righteousness.
and again
isaiah 48:10
Behold, I have refined thee, but not with silver; I have chosen thee in the furnace of affliction.
and again
deut 4:20
But the Lord hath taken you, and brought you forth out of the iron furnace, even out of Egypt, to be unto him a people of inheritance, as you are this day.
Let me discuss now the other part of your opening post about God being an all consuming fire.
Nothing impure can exist in the immediate and full Presence of God. Any impure thing would vanish. Poof, up in smoke.
Habakkuk 1:13 Thou art of purer eyes than to behold evil, and canst not look on iniquity. . . .
God Himself does not see anything impure, not directly. His angels see and intervene. This explains the need for mediators. I think it explains the need for a Messiah. God protects us by keeping us "at a distance" so to speak. If a sinner were to be in His Presence, he could go out of existence. So it is out of Mercy that God has this distance. If we purify ourselves as we can, we are using the Flames of Mercy to do it. We are trying to get closer to God, and He responds by coming closer to us.
James 4:8 Draw nigh to God, and he will draw nigh to you. Cleanse your hands, ye sinners; and purify your hearts, ye double minded.
I believe on Judgment Day, any remaining impurities we have will be burned away. It's like rotten wood being burned; but after the final judgment, we won't be able to grow "new wood." Thus Paul talks about someone being saved himself but still losing some things.
1 Corinthians 3:13 Every man's work shall be made manifest: for the day shall declare it, because it shall be revealed by fire; and the fire shall try every man's work of what sort it is.
14 If any man's work abide which he hath built thereupon, he shall receive a reward.
15 If any man's work shall be burned, he shall suffer loss: but he himself shall be saved; yet so as by fire.
Life is precious then. We are given the opportunity to "lay up treasures in Heaven" as Jesus said by purifying ourselves now when we see a vice that can be replaced by a virtue. By giving it up to the Sacred Fires now, we still have a chance to gain a virtue that won't be burnt up on the day of testing we pass through the flames. We are told to "buy gold tried in the fire" now.
Revelation 3:18 I counsel thee to buy of me gold tried in the fire, that thou mayest be rich; and white raiment, that thou mayest be clothed, and that the shame of thy nakedness do not appear; and anoint thine eyes with eyesalve, that thou mayest see.
Those who say Jesus is going to do it all for them may be disappointed later.