So therefore, Holy Communion is about Communion with the Roman Catholic Church and not about Communion with the Lord?
Eastern Orthodox Christians, by the way, are allowed by Rome to receive Communion in Roman Catholic Churches (they are, however, not allowed by their own churches to receive in Roman Catholic Churches).
No, that is not what I said. I said that communion with the Catholic Church is one of several criteria in order for one to receive Holy Communion at a Catholic Mass. Another criterion is that a Catholic must be in a state of grace (or as you put it "in communion with the Lord") in order to receive Holy Communion. This means that if one has committed a mortal sin (committed a grave act with knowledge - that it is a grave matter - and full consent) and not gone to confession, then one cannot receive Holy Communion. If one's soul is in a state of mortal sin and one receives Holy Communion, then one has committed a sacrilege which is another mortal sin. Catholics who are not in a state of grace cannot receive Holy Communion at a Catholic Mass.
It is out of charity that the Catholic Church does not allow non-Catholics from non-Apostolic faiths to receive Holy Communion. They would be condemning themselves since many of them do not believe that the Eucharist is truly the Body, Blood, Soul and Divinity of Jesus Christ which is what the Catholic Church believes and teaches.
Why would one who doesn't believe what the Church believes want to receive Holy Communion at a Catholic Mass?