It is not so much that Rome has lost it's lineage of apostolic succession but rather it has lost grace of apostolic succession by abandonment of the apostolic faith. The Orthodox Church can trace its externals and internals (doctrines, the Gospel) to the 1st century Church. For example St. Augustine, whom did not know Greek and was raised Gnostic and later converted to Christianity, and because he was unable to read Greek and read the Fathers in Greek nor read the New Testament in its original Greek, which he used a bad Latin translation of the Bible and had known Gnosticism for most of his life; certain ideas developed in Augustine's thought which were very harmful to the later development of the Western Church. Among these are original sin, predestination, irresistible grace and the filiqoue which eventually worked its way into Western thought and ultimately the bad will and further distortion by some men the Western Church separated from the Orthodox Church. And other further divisions can be expounded upon by the likes of St Jerome who I've heard argued did more harm than Augustine did.
It's not that the Roman church didn't exist in the 1st century, it is rather that the Roman church taught, preached, and proclaimed the Orthodox Christian understanding of the Gospel rather than the contemporary Roman Catholic understanding of the Gospel. To put it simply Rome abandoned the Fathers and replaced them with the Scholastics, that's why the modern Roman Catholic church cannot be traced to the 1st century.
It's not that the Roman church didn't exist in the 1st century, it is rather that the Roman church taught, preached, and proclaimed the Orthodox Christian understanding of the Gospel rather than the contemporary Roman Catholic understanding of the Gospel. To put it simply Rome abandoned the Fathers and replaced them with the Scholastics, that's why the modern Roman Catholic church cannot be traced to the 1st century.