What is the Biblical basis for saying the Apostles did not necessarily expect the final judgment to occur in their lifetime?

The apostle John provided a word of caution, showing a bit of a misunderstanding on the part of the apostle Peter regarding Christ returning soon. This is in John's gospel account, at the end. After his resurrection, while at the Sea of Tiberias, Jesus had signified how Peter's future death would glorify God. Peter then asked, 'What about John?' This is John's record of the event:

"Jesus saith unto [Peter], If I will that [John] tarry till I come, what is that to you?" Then went this saying abroad among the brethren, that that disciple should not die; yet Jesus said not unto him, 'He shall not die'; but 'If I will that he tarry till I come, what is that to thee?' (John 21:18-23)

The error of the disciples is shown by John. Peter was told he would die; John was to tarry - the wrong conclusion jumped to was that John would not die. When Jesus spoke about him tarrying, John had been about 30 to 35 years of age. Here is how the book below puts it:

"From that moment until the writing of the fourth gospel and the three epistles, but above all until the setting down of this book [Revelation], John tarried. Then Jesus came, appearing by his angel to give the Revelation of Jesus Christ to his slave John.

John tarried: but the reason was that he was constrained by a spiritual discipline virtually unknown in church history and certainly unknown at the present time... It was simply that the Lord willed that he should tarry... Contemplative, silent; waiting; in effect, tarrying for a lifetime. And, as a lifetime slipped away, it must have seemed tarrying for ever.

Some forty years after Jesus spoke the words quoted in John 21:22, Jerusalem was destroyed and the remaining apostles were scattered. John, by then about seventy years of age, now made homeless as to Jerusalem, tarried still.

The persecutions of Nero came and went. More to the point, the ministry of the apostle Paul arose so mightily, finally to pass away. Yet for this man, John, by now beyond normal old age, really an ancient, tarrying remained.

John had survived the first generation, and seen the passing away of the second generation as that in turn aged and departed. John had endured the persecutions of Nero. He had seen the end of the apostles, Paul included, long, long ago. But now storm clouds began to gather again. Under the Roman Emperor Dominitan the fires of persecution were rekindled.

The Dominitan persecutions raged from the year 81 to 86. During this period the last apostle, John, was banished to the remote Island of Patmos. This was about the year 95. This approximated to the great age of the apostle. It was also about the time in which at long last there came the conclusion to John's seemingly endless 'tarrying'.

Finally, in the Spirit, and by his angel, the Lord came for John, and came that he might render the last, the great, the consummate witness of the new testament, till time should be no more. [Rev. 10:6] It was for this, the Revelation of Jesus Christ... that the slave of Jesus Christ had been kept for longer than might be considered endurable or even possible. But by the grace of the Spirit he had been kept; by the grace of Christ he had endured; and by the grace of God he had submitted. Now at length he was called to render the most momentous, the mostly overwhelming testimony of all the sixty-six books of the Holy Bible, with which the whole was to be brought to its fitting conclusion." (The Revelation of Jesus Christ, John Metcalfe, pp.2-4)

Once John had discharged his final duty and written the whole of that Revelation to be distributed to the congregations in Asia Minor, he - the last surviving apostle - would know that the final judgment would not occur in his lifetime. So would all the other Christians, none of whom were apostles. They would all know that various events would have to now happen, culminating in the final judgment. They would know the churches were repeatedly told to endure, to hold fast, to overcome (chapters 2 & 3). That would take time.

Therefore, in addition to other new testament scriptures - 1 Peter 3:7-15 & Revelation 6:9-11 - all Christians on the cusp of the second century A.D. would surely understand that more had to happen, with only one very elderly apostle still alive (though not for much longer).