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I do not say, indeed, that all souls die. That would truly be a piece fo good fortune to evil people. What then? The souls of the godly remain in a better place, while those of the unrighteous and wicked are in a worse place, waiting for the time of judgment. Thus some which have appeared worthy of God never die, but others are punished so long as God wills them to exist and be punished. (Dialogue with Trypho, a Jew 5)

This is Trypho, the Jew, speaking in dialogue with Justin, so it represents Jewish, but not necessarily Christian, thinking.

The soul partakes of life, since God wills it to live. Thus, then, it will not partake when God does not will it to live. For to live is not its attribute, as it is God's. Instead, as a man does not live always, and the soul is not joined with the body forever, then whenever this harmony must be broken up, the soul leaves the body, and the man exists no longer. Even so, when the soul must cease to exist, the spirit of life is removed from it, and there is no more soul, but it goes back to the place from where it was taken. (Dialogue with Trypho, a Jew 6)

The Lord has taught with very great fullness, that souls not only continue to exist, not by passing from body to body, but that they preserve the same form as the body had to which they were adapted, and that they remember the deeds which they did in this state of existence, and from which they have now ceased in that narrative which is recorded respecting the rich man and that Lazarus who found repose in the bosom of Abraham. In this account He states that Dives [Latin for "rich man"] knew Lazarus after death, and Abraham in like manner, and that each one of these persons continued in his own proper position, and that he requested Lazarus to be sent to relieve him—he on whom he did not bestow even the crumbs from his table.

[The Lord tells us] also of the answer given by Abraham, who was acquainted not only with what respected himself, but the rich man also, and who enjoined those who did not wish to come into that place of torment to believe Moses and the prophets, and to receive the preaching of Him who was to rise again from the dead [Luke 16:19-31].

By these things, then, it is plainly declared that souls continue to exist, that they do not pass from body to body, that they possess the form of a man, so that they may be recognized, and retain the memory of things in this world; moreover, that the gift of prophecy was possessed by Abraham, and that each class [of souls] receives a habitation such as it has deserved, even before the judgment. (Against Heresies, Bk. II, ch. 34, par. 1)

Note that this quote is about martyrs. The early churches believed martyrs did not have to face the final judgment.

To myself also, the very least and last, how often it has been revealed, how frequently and manifestly has it been commanded by the condescension of God, that I should diligently bear witness and publicly declare that our brethren who are freed from this world by the Lord's summons are not to be lamented, since we know that they are not lost, but sent before; that, departing from us, they precede us as travelers, as navigators are accustomed to do. They should be desired, but not bewailed. The black garments should not be taken upon us here, when they have already taken upon them white raiment there. (On Mortality, par. 20)

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