2 John 1:5

We come now more into the design and substance of the epistle; and here we have, I. The apostle's request: Now, I beseech thee, lady. Considering what it is that he entreats, the way of address is very remarkable; it is not any particular boon or bounty to himself, but common duty and observance of divine command. Here he might command or charge; but harsher measures are worse than needless where milder will prevail; and the apostolical spirit is, of all other, the most tender and endearing. Whether out of deference to her ladyship, or apostolical meekness, or both, he condescends to beseech: And now I beseech thee, lady. He may be supposed speaking as another apostle does to a certain master to whom he writes: Wherefore, though I might be very bold in Christ (and according to the power with which Christ hath entrusted me) to enjoin thee that which is convenient, yet, for love's sake I rather beseech thee, being such a one as the aged, the elder. Love will avail where authority will not; and we may often see that the more authority is urged the more it is slighted. The apostolical minister will love and beseech his friends into their duty. II. The thing requested of the lady and her children - Christian sacred love: That we love one another, Jo2 1:5. Those that are eminent in any Christian virtue have yet room to grow therein.

— Matthew Henry's Concise Commentary (public domain)

I beseech--rather (compare Note, see on Jo1 5:16), "I request thee," implying some degree of authority. not . . . new commandment--It was old in that Christians heard it from the first in the Gospel preaching; new, in that the Gospel rested love on the new principle of filial imitation of God who first loved us, and gave Jesus to die for us; and also, in that love is now set forth with greater clearness than in the Old Testament dispensation. Love performs both tables of the law, and is the end of the law and the Gospel alike (compare Notes, see on Jo1 2:7-8). that we--implying that he already had love, and urging her to join him in the same Christian grace. This verse seems to me to decide that a Church, not an individual lady, is meant. For a man to urge a woman ("THEE"; not thee and thy children) that he and she should love one another, is hardly like an apostolic precept, however pure may be the love enjoined; but all is clear if "the lady" represent a Church.

— Jamieson-Fausset-Brown Commentary (public domain)