Lady (kuria). Vocative case and in the same sense as in 2Jo 1:1.
As though I wrote (hōs graphōn). Common idiom hōs with the participle (present active) for the alleged reason.
New (kainēn). As in 1Jo 2:7., which see.
We had (eichamen). Imperfect active (late ̇a form like eichan in Mar 8:7) of echō and note eichete with ap' archēs in 1Jo 2:7. Not literary plural, John identifying all Christians with himself in this blessing.
That we love one another (hina agapōmen allēlous). Either a final clause after erōtō as in Joh 17:15 or an object clause in apposition with entolēn, like 1Jo 2:27; 1Jo 3:23 and like 2Jo 1:6.