In your question, it would be best to use the precise expression ‘Roman Catholic Church’ instead of ‘Catholic Church’ since we Orthodox apply this expression to ourselves! The question of when a (local) Church ceases to become an assured manifestation of the Body of Christ is to an extent the topic of Revelation 2 and 3, with the Lord’s threat “If you do not repent, I will come to you and remove your lampstand from its place.” Actually, this can be true of an Orthodox community as well, which can “fall” into immorality, corruption and heresy.
From an Orthodox perspective, the Church in Lisbon (taken as our example) has its own life and identity apart from the Church of Rome, although after the Gregorian reform (11th century) it is true that the Churches of West were almost absorbed by the Roman Church. When then did the (Latin/Catholic) Church in Lisbon cease being the Church or an assured manifestation of the Church? It is hard to say (some may say never) and this requires pastoral judgment when the need arises. One may say that there is only one historic, apostolic, Eucharistic community in Lisbon (the Roman Catholic one – since there is no Orthodox bishop of Lisbon). However, an Orthodox Christian would say that the theology, ecclesiology and sacramental life of the Church in Lisbon is gravely impaired and defective. (Honesty would require us to say that at times, the same can be said of Orthodox Churches, as when the people only communed once a year and when the theology was fully Westernized).
For this reason, an Orthodox bishop who would receive a Christian (a Roman Catholic) from Lisbon would consider the applicable canons and use his judgment as pastor. In order to maximize assurance of incorporation into the Body of Christ, the bishop may require or suggest (re)rebaptism or conditional rebaptism (“if not already baptized, the servant of God N. is baptized in the Name…”) since the first one was bare-bones, by sprinkling, not done with the fullness of Orthodox understanding of the mystery of baptism, or simply “seal” the baptism with Holy Chrism and the Eucharist. Since the bishop is “head slave” in the Lord’s house, economia literally means that he manages the house (the Church or Diocese) according to what he thinks is best for the person’s salvation and the good order of the Church, in consultation with his presbyters and fellow-bishops.
