I think my EO brothers and sisters may be overplaying the "we don't need a second lung" thing... To be blunt, we absolutely do need both lungs to breath (we need the fullness of the faith), and we absolutely already have them. The issue we have with the two lungs theory is that it implies that, somewhere along the way, the fullness of the Catholicity of the faith was lost. Even for the west this would be true, as between 1054 (or 1204 if you prefer) and 1453 (Florence) there wasn't an Eastern Rite in communion with Rome. You would, then (if you find us so insufficient for not having the western rite) have to admit that, at that time, YOU were insufficient for not having an eastern rite.
In other words, if we insist on "catholic" as meaning "having east and west" then we would BOTH have to admit that we ceased to be "catholic" in the middle ages. Neither church really feels that way, and so we find the two lungs analogy (when pressed) to just fall short as a definition of "catholicity."
Catholicity is not found exclusively within the diversity of one's worship expression, but if you are so concerned about it, then know that there is a Western Rite within Orthodoxy - mostly Anglican communities that have rejoined the Orthodox Church. We have both East and West. And there are WESTERNERS who happen to use the liturgy of St. John Chrysostom. I am one of them. But I am no more Eastern than any other person living on the West Coast of the US. CULTURE isn't the same as style of worship either. The Orthodox church IS global, if that's your definition of Catholic, so there isn't a concern there either. We have churches on all continents (except Antarctica, I think), and are more than our mere autocephalous churches.
The word Catholic, though, doesn't mean "all over the world" or "incorporating all peoples." The word Catholic, as used in the Creed, refers to the Church's holistic nature (that it supplies, by God's grace, all things needed for salvation). The word universal (oecumene) is meant to imply "worldwide." But even at the time, this was not literal (rather, it implies that the faith is for the whole world - not in the whole world).
Yet one loses the catholicity of the faith and its universality if one abandons the traditional faith (by which I mean beliefs and practices). If the faith of Nicaea (and pre-Nicaea) was Catholic (holistic / complete) and Universal (intended for all), then it is to THAT faith which we must adhere.
I'm not certain the RCC understands it the same way, but I wanted to clarify what we understand Catholicity to mean, and why we (therefore) reject the two-lungs analogy. It isn't because we don't want the Western Rite, we do - we just want the RCC to confess again what we view as the traditional faith.
Hope that helps, forgive me if I offend...
In Christ,
Macarius