2nd John 1:1

2nd John 1:1-6 (see also 2nd John 1:13)
The elder to the chosen lady and her children, whom I love in truth; and not only I, but also all who know the truth, for the sake of the truth which abides in us and will be with us forever: Grace, mercy and peace will be with us, from God the Father and from Jesus Christ, the Son of the Father, in truth and love. I was very glad to find some of your children walking in truth, just as we have received commandment to do from the Father. Now I ask you, lady, not as though I were writing to you a new commandment, but the one which we have had from the beginning, that we love one another. And this is love, that we walk according to His commandments. This is the commandment, just as you have heard from the beginning, that you should walk in it. 

4-Point Calvinist, Ron Rhodes: “It is likely that this lady was not a human being but rather a churchThe church is called a chosen lady because it is made up of God’s elect believers. The lady’s children are the individual members of the church. The reference to the chosen sister (verse 13) may well point to John’s own church congregation. John probably called the church a lady because of the possibility that the letter could be intercepted by Roman authorities while en route. If that happened, the letter might give these authorities enough information to capture and imprison the Christians (or worse). Calling the church a lady was therefore a simple safety measure.” (Commonly Misunderstood Bible Verses, p.279, emphasis mine)

​2nd John 1:13: “The children of your chosen sister greet you.

This explanation is highly plausible. Also note the comment of “God’s elect believers,” since I agree with Lawrence Vance that there is no such thing as an elect un-believer:

Laurence Vance: “There is no such animal as an ‘elect unregenerate’ child of God.” (The Other Side of Calvinism, p.336, emphasis mine)