The final section of St John's Gospel is an autobiographical note on the 'beloved disciple' (St John himself).
The New Advent page can be found here. The Latin is:
20 Conversus Petrus vidit illum discipulum, quem diligebat Jesus, sequentem, qui et recubuit in cœna super pectus ejus, et dixit: Domine, quis est qui tradet te? 21 Hunc ergo cum vidisset Petrus, dixit Jesu: Domine, hic autem quid? 22 Dicit ei Jesus: Sic eum volo manere donec veniam, quid ad te? tu me sequere. 23 Exiit ergo sermo iste inter fratres quia discipulus ille non moritur. Et non dixit ei Jesus: Non moritur, sed: Sic eum volo manere donec veniam, quid ad te? 24 Hic est discipulus ille qui testimonium perhibet de his, et scripsit hæc: et scimus quia verum est testimonium ejus. 25 Sunt autem et alia multa quæ fecit Jesus: quæ si scribantur per singula, nec ipsum arbitror mundum capere posse eos, qui scribendi sunt, libros.
Peter turning about, saw that disciple whom Jesus loved following, who also leaned on his breast at supper, and said: Lord, who is he that shall betray thee? Him therefore when Peter had seen, he saith to Jesus: Lord, and what shall this man do?  Jesus saith to him: So I will have him to remain till I come, what is it to thee? follow thou me.  This saying therefore went abroad among the brethren, that that disciple should not die. And Jesus did not say to him: He should not die; but, So I will have him to remain till I come, what is it to thee?  This is that disciple who giveth testimony of these things, and hath written these things; and we know that his testimony is true.  But there are also many other things which Jesus did; which, if they were written every one, the world itself, I think, would not be able to contain the books that should be written.
Catena Aurea on the beloved disciple:
AUG. He calls himself the disciple whom Jesus loved, because Jesus had a greater and more familiar love for him, than for the rest; so that He made him lie on His breast at supper. In this way John the more commends the divine excellency of that Gospel which he preached.
Some think, and they no contemptible commentators upon Scripture, that the reason why John was loved more than the rest, was, because he had lived in perfect chastity from his youth up. Then went this saying abroad among the brethren, that that disciple should not die: yet Jesus said not to him, He shall not die; but, If I will that he tarry till I come, what is that to you?
THEOPHYL. i.e. Shall he not die?
AUG. Jesus says to him, What is that to you? and He then repeats, Follow you Me, as if John would not follow Him, because he wished to remain till He came; Then went this saying abroad among the disciples, that disciple should not die. Was it not a natural inference of the disciple's? But John himself does awes With such a notion: Yet Jesus said not to him, He shall not die; but, If I will that he tarry till I come, what is that to you? But if any so will, let him contradict, and say that what John says is true, viz. that our Lord did not say that that disciple should not die, but that nevertheless this was signified by using such words as John records.
THEOPHYL. Or let him say, Christ did not deny that John was to die, for whatever is born cries; but said, I will that he tarry till I come, i.e. to live to the end of the world, and then he shall suffer martyrdom for Me. And therefore they confess that he still lives, but will be killed by Antichrist, and will preach Christ's name with Elias. But if his sepulcher be objected, then they say that he entered in alive, and went out of it afterwards.
AUG. Or perhaps he will allow that John still lies in his sepulcher at Ephesus, but asleep, not dead; and will give us a proof, that the soil over his grave is moist and watery, owing to his respiration. But why should our Lord grant it as a great privilege to the disciple whom He loved, that he should sleep this long time in the body, when he released Peter from the burden of the flesh by a glorious martyrdom, and gave him what Paul had longed for, when he said, I have a desire to depart and be with Christ? If there really takes place at John's grave that which report says, it is either done to commend his precious death, since that had not martyrdom to commend it, or for some other cause not known to us. Yet the question remains, Why did our Lord say of one who was about to die, I will that he tarry till I come? It may be asked too why our Lord loved John the most, when Peter loved our Lord the most? I might easily reply, that the one who loved Christ the more, was the better man, and the one whom Christ loved the more, the more blessed; only this would not be a defense of our Lord's justice. This important question then I will endeavor to answer. The Church acknowledges two modes of life, as divinely revealed, that by faith, and that by sight. The one is represented by the Apostle Peter, in respect of the primacy of his Apostleship; the other by John: wherefore to the one it is said, Follow Me, i.e. imitate Me in enduring temporal sufferings; of the other it is said, I will that he tarry till I come: as if to say, Do you follow Me, by the endurance of temporal sufferings, let him remain till I come to give everlasting bliss; or to open out the meaning more, Let action be perfected by following the example of My Passion, but let contemplation wait inchoate till at My coming it be completed: wait, not simply remain, continue, but wait for its completion at Christ's coming. Now in this life of action it is true, the more we love Christ, the more we are freed from sin; but He does not love us as we are, He frees us from sin, that we may not always remain as we are, but He loves us heretofore rather, because hereafter we shall not have that which displeases Him, and which He frees us from. So then let Peter love Him, that we may be freed from this mortality; let John be loved by Him, that we may be preserved in that immortality. John loved less than Peter, because, as he represented that life in which we are much more loved, our Lord said, I will that he remain (i.e. wait) till I come; seeing that that greater love we have not yet, but wait till we have it at His coming. And this intermediate state is represented by Peter who loves, but is loved less, for Christ loves us in our misery less than in our blessedness: and we again love the contemplation of truth such as it will be then, less in our present state, because as yet we neither know nor have it. But let none separate those illustrious Apostles; that which Peter represented, and that which John represented, both were sometime to be.
CHRYS. John appeals to his own knowledge of these events, having been witness of them: This is the disciple which testifies of these things. When we assert any undoubted fact in common life, we do not withhold our testimony: much less would he, who wrote by the inspiration of the Holy Ghost. And thus the other Apostles, And we are witnesses of these things, and wrote these things. John is only one who appeals to his own testimony; and he does so, because he was the last who wrote. And for this reason he often mentions Christ's love for him, i.e. to show the motive which led him to write, and to give weight to his history. And we know that his testimony is true. He was present at every event, even at the crucifixion, when our Lord committed His mother to him; circumstances which both show Christ's love, and his own importance as a witness.
There is more to the tradition than contained in Scripture:
CHRYS: But if any believe not, let him consider what follows:
And there are also many other things which Jesus did. If, when there were so many things to relate, I have not said so much as the other, and have selected often reproaches and contumelies in preference to other things, it is evident that I have not written partially. One who wants to show another off to advantage does the very contrary, omits the dishonorable parts.
AUG. The which, if they should be written every one, I suppose that even the world itself could not contain the books that should, be written; meaning not the world had not space for them, but that the capacity of readers was not large enough to hold them: though sometimes words themselves may exceed the truth, and yet the thing they express be true; a mode of speech which is used not to explain an obscure and doubtful, but to magnify or estimate a plain, thing: nor does it involve any departure from the path of truth; inasmuch as the excess of the word over the truth is evidently only a figure of speech, and not a deception. This way of speaking the Greeks call hyperbole, and it is found in other parts of Scripture.
CHRYS. This is said to show the power of Him Who did the miracles; i. e that it was as easy for Him to do them, as it is for us to speak of them, seeing He is God over all, blessed for ever.
And that concludes this series of lectio notes on the Gospel of St John. I hope that it has stimulated you to do more lectio divina; that the notes proved helpful, and your reading proved fruitful!