There are no shortage of florilegia/quote mines on the issue of extra Ecclesiam nulla salus (“no salvation outside the Church”). Though the issue is not entirely without support from eastern fathers, it appears to be more of an emphasis among the western fathers who dealt with long term schisms among the Novationists and Donatists.
My small contribution to this subject is a short compilation of fathers who teach on the typology of the Ark of Noah being the Church and what that entails. Only one eastern father (Saint Firmilian) picks up on the idea and he almost certainly was reiterating what he had read in Saint Cyprian’s writings. From Cyprian, the western tradition appears to reiterate the idea of “no salvation outside the Church” whenever Noah’s Ark comes up. The other popular teachings on the subject revolve around baptism and the Church having both saved and unsaved (i.e. clean and unclean animals, two saved sons of Noah and one cursed one). Eastern treatments of Noah’s Ark (including Saints Ephraim, Cyril of Jerusalem, John Chrysostom, and Damascene) tend to be more literalistic, drawing only moral lessons from what they iterated to be a historical event. Saint Ambrose is similar to the eastern fathers in this regard, though I have not read On Noah in which to conclude this with absolute certainty.
Ironically, the Pan-Orthodox Council of Jerusalem (1672) in the minutes of the council ends up quoting approvingly a passage of Cyril Lukaris on the question with the intent of proving that Lukaris did not believe in Protestantism. If he did, the council appears to speculate, why would he exclude their salvation? And so, this mostly-western typological interpretation ultimately appears to attain a conciliar approval and application on the question of there being (as the doctrine is called) “no salvation outside the Church.”
This quote mine is not intended to definitively address the question of “no salvation outside the Church.” As follows are passages concerning the Ark of Noah, all of which can be easily verified on New Advent if their citations do not contain links to other sources:
And as the Ark of Noah was nothing else than the sacrament of the Church of Christ, which then, when all without were perishing, kept those only safe who were within the ark, we are manifestly instructed to look to the unity of the Church. Even as also the Apostle Peter laid down, saying, Thus also shall baptism in like manner make you safe; 1 Peter 3:21 showing that as they who were not in the ark with Noah not only were not purged and saved by water, but at once perished in that deluge; so now also, whoever are not in the Church with Christ will perish outside, unless they are converted by penitence to the only and saving lava of the Church. (Saint Firmilian quoted in Cyprian, Epistle 74:15)
He can no longer have God for his Father, who has not the Church for his mother. If any one could escape who was outside the Ark of Noah, then he also may escape who shall be outside of the Church. The Lord warns, saying, He who is not with me is against me, and he who gathers not with me scatters. Matthew 12:30 He who breaks the peace and the concord of Christ, does so in opposition to Christ; he who gathers elsewhere than in the Church, scatters the Church of Christ. (Saint Cyprian, Treatise 1:6)
As I follow no leader save Christ, so I communicate with none but your blessedness, that is with the chair of Peter. For this, I know, is the rock on which the church is built! Matthew 16:18 This is the house where alone the paschal lamb can be rightly eaten. Exodus 12:22 This is the Ark of Noah, and he who is not found in it shall perish when the flood prevails. (Saint Jerome, Letter 15:2)
But I have the sacrament, you will say. You say the truth; the sacrament is divine; you have baptism, and that I confess. But what says the apostle? If I should know all mysteries, and have prophecy and all faith, so that I could remove mountains; in case you should say this, I believe; enough for me. But what says James? The devils believe and tremble. James 2:19 Faith is mighty, but without charity it profits nothing. The devils confessed Christ. Accordingly it was from believing, but not from loving, they said, What have we to do with You? Mark 1:24 They had faith, but not charity; hence they were devils. Boast not of faith; so far you are on a level with the devils. Say not to Christ, What have I to do with You? For Christ’s unity speaks to you. Come, learn peace, return to the bowels of the dove. You have been baptized without; have fruit, and you return to the ark. But do you say, Why do you seek us if we are bad men? That you may be good. The reason why we seek you is, because you are bad; for if you were not bad, we should have found you, and would not be seeking you. He who is good is already found; he who is bad is still sought after. Consequently, we are seeking you; return ye to the ark. But I have baptism already. Though I should know all mysteries, and have prophecy and all faith, so as to remove mountains, but have not charity, I am nothing. Let me see fruit there; let me see the olive there, and you are called back to the ark. (Saint Augustine, Tractate on John 6:21-22)
Heretics doubtless, when they come back from their error, cannot appease the wrath of God towards them by a sacrifice offered by themselves, unless they are converted to the Catholic Church, which blessed Job designates…For it is she alone through whom God willingly accepts a sacrifice, she alone who intercedes with confidence for those who are in error. Whence also the Lord commanded concerning the sacrifice of the lamb, saying; In one house it shall be eaten, neither shall ye carry forth of the flesh thereof out of the house. [Ex. 12, 46] For the lamb is eaten in one house, because the true Sacrifice of the Redeemer is immolated in the one Catholic Church. And the Divine law orders its flesh not to he carried forth abroad, because it forbids that which is holy to be given to dogs. [Matt. 7, 6] It is she alone in whom a good work is fruitfully carried on, whence they only who had laboured in the vineyard received the reward of a penny. [Matt. 20, 10] It is she alone who guards those who are placed within her by the strong bond of charity. Whence also the water of the deluge raised the ark indeed aloft, but destroyed all those whom it found out of the ark. It is she alone in whom we truly contemplate the heavenly mysteries. (Saint Gregory the Great, Moralia on Job, Book 35:12-13; cf Registrum Epistolarum, Book 11, Letter 46)
‘For the Ark was wide on the lower decks, and narrow on the higher decks.’ For also those inside the Church who continually run down a wide and spacious road may be called not humans but beasts. They are meant by the unclean animals, two by two. Yet ‘the men and birds are kept on the upper decks.’ They who are capable of reason are called men; the birds in this place are understood to be those who stay in contemplation of the faith. And just as ‘the eight souls’ and the beasts and the birds in the Ark relied on the one Ark to be saved, so it is in ‘the Church’. (Saint Beatus of Liébana, Catena on Rev 1:13)
And just as, after the ark was made all those creatures that were saved were brought into it, the flood came and and carried off all those that were outside of it, so when all people who have been predestined for eternal life have entered the Church, the end of the world will come, and all the people found outside the Church will perish. And in this sense, the Ark clearly signifies the Church, Noah signifies the Lord that builds the Church in his saints, and the flood signifies the end of the world or the Last Judgement. (Saint Bede, On Genesis, p. 173)
Noah was shown to be the saviour, not of all the race of men in general, but of his own household, all of whom were saved through him. In the same way Christ, too, is the Saviour of the race of men, not of all men in general, but of His own household, that is of the Church; not, however, of the disobedient. (Saint Gregory Palamas, Homily 57:9, p. 471 in Venamin’s translation)
In closing, the following from Cyril Lukaris is quoted by the Council of Jerusalem as proof he did not really write the confession ascribed to him. The second chapter of the confession is as follows:
We believe the Holy Scripture to be given by God, to have no other author but the Holy Spirit. This we ought undoubtedly to believe, for it is written. We have a more sure word of prophecy, to which you do well to take heed, as to light shining in a dark place. We believe the authority of the Holy Scripture to be above the authority of the Church. To be taught by the Holy Spirit is a far different thing from being taught by a man; for man may through ignorance err, deceive and be deceived, but the word of God neither deceives nor is deceived, nor can err, and is infallible and has eternal authority. (Source)
To prove the preceding is not so, Lukaris is quoted approvingly as follows, thereby cloaking the preceding typological interpretations with the conciliar approval of the Orthodox Church:
As none can sail across the sea without a boat, so thou canst not steer through this world and its billows, and escape them, without a boat, which is the Church of Christ. Many endeavour to sail across it [the sea]; such are the impious and all the heretics, who are not within the Church of God, but they are all drowned. When God made the Ark, all that were within escaped, while those that were without perished. The Church of God is this Ark. (The Synod of Jerusalem , p. 25)