I think I can see your point in part.
If we start with the assumption that the Eastern lung is either the Eastern Catholics or the Eastern Orthodox,
then I can agree that Ut Unum Sint is more compatible with it being the Eastern Orthodox.
However, it seems to me to be just as compatible with the idea that the two lungs are the Western heritage and Eastern heritage of the Church.
So at this point, we need to look to other sources for deciding between two reasonable interpretations. For me personally, I prefer the “heritage” interpretation, because the alternative comes too close to “Branch Theory” (which is just as unacceptable to the Orthodox as it is to Catholics) for my comfort.
Or to further expound it, you see more the past–that is, the heritage or patrimony–of the East as the other lung, which is not necessarily the Orthodox Church.
Our heritage is
rooted in the past, but it comes to us through living churches: the Eastern lung is a heritage which comes to us through the Eastern Catholic Churches, Eastern Orthodox Churches, Oriental Orthodox Churches, Assyrian Church of the East, etc. The Western lung is a heritage which comes to us through the Latin Catholic Church, WRO, SSPX, PNCC, Old Catholic Churches, etc. (Even the Anglicans and Protestants, although lacking Orders, carry on the Western heritage in some ways.)