Here our author mentions that he noted the succession of Bishops at Rome, but he gives his list with no remark about Rome in particular. He adds that "in every succession and in every city (i.e., in every See) a primitive accordance with the law and the Gospel is maintained." How can our excellent Lightfoot  give it a colour wholly gratuitous in these words: "He interested himself in the succession of the Roman See, intent, like Irenæus in the next generation, on showing the permanence of the orthodox tradition, through the continuity of the Roman episcopate." Irenæus, who, above all the Westerns, is identified with the Orient!
Where is the evidence of any such idea or "intent"? As for Irenæus, his testimony has been sufficiently illustrated before, with proof that his words have not the slightest reference to the continuity of the Roman more than any other See, save only as the influx of visitors from other Sees helped to give it orthodoxy by their concurrent testimony. 
 Ap. Fathers, part ii. vol. i. p. 435; and the same laxity, p. 384, coincident with his theory as to a virtual post-Apostolic development of episcopacy.  Compare vol. i. pp. 415, 460, and vol. v. Elucid. VI.; also Elucid. XI. pp. 157-159, this series.
 Compare vol. i. pp. 415, 460, and vol. v. Elucid. VI.; also Elucid. XI. pp. 157-159, this series.