Real Bible Translation

The Elder to a chosen/selected lady,¹ and the Children of herself, which ones I, myself am agape-loving within a truth, and not myself alone, but also all those who have recognized the Truth!

LITV Translation:
The elder to the elect lady and her children, whom I love in truth; and not I only, but also all those who have known the truth,

ESV Translation:
The elder to the elect lady and her children, whom I love in truth, and not only I, but also all who know the truth,

Footnotes

The Greek term κύριος (masculine) refers to "lord," "master," or "owner," denoting authority or control. Its feminine form used in 2 John, κυρία, similarly signifies lady or mistress as having authority over the House (of God).

It is also used in the sense of "authority," "power," or "possession":

"μηδὲ πλῆθος συστραφὲν ἐπ᾿ αὐτῶν ἐπὶ τὴν νῆσον κυρίας τύχῃ καὶ τὴν τῶν Καρχηδονίων εὐδαιμονίαν ἀφέληται."
Translation:
"Nor should a multitude gathered against them gain mastery over the island and take away the prosperity of the Carthaginians."

(Aristotle's Mirabilia (On Marvellous Things Heard) 837a5)

Or as "authoritative style/expression":

"Κέχρηται δὲ λέξει κυρίᾳ κατὰ τῶν πραγμάτων, ἣν ὅτι ἰδιωτάτη ἐστίν, Ἀριστοφάνης ὁ..."

"He has employed an authoritative style of expression concerning the matters, which, because it is particularly straightforward, Aristophanes..."

(Diogenes Laertius, Lives of Eminent Philosophers (Book 10, Chapter 1))

Or as "critical/decisive":

"νεανίσκοι ταῦτ᾽ ἐπαινέσαντες καὶ κατὰ τὰ συγκείμενα παρῆσαν ἐν τῇ κυρίᾳ τῆς πράξεως ἡμέρᾳ. ἦν δὲ Ῥωμύλῳ μὲν οἰωνιστήριον, ἔνθα…"

"The young men, having praised these things, and according to what had been agreed upon, were present on the decisive day of the action. For Romulus, there was an omen at that place..."

(Dionysius of Halicarnassus, Antiquitates Romanae (Book 1, Chapter 86))

Or as "control" over specific domains, such as property or roles (Plb. 6.13.1, 6.14.10).

"καὶ μὴν ἡ σύγκλητος πρῶτον μὲν ἔχει τὴν τοῦ ταμιείου κυρίαν."

"And indeed, the Senate first holds the authority over the treasury."

(Polybius' Histories, Book 6, Section 11A)

In terms of a lady or mistress, it was a powerful word, even used to condition or manipulate young women into believing they possessed authority solely by fulfilling certain outward appearances and roles, often tied to superficiality and sex. Epictetus (Stoicism) critiqued this cultural tendency, which valued women (and people in general) based on outward appearances, suggesting instead that they should seek honor in their inner character and self-respect:

αἱ γυναῖκες εὐθὺς ἀπὸ τεσσαρεσκαίδεκα ἐτῶν ὑπὸ τῶν ἀνδρῶν κυρίαι καλοῦνται. τοιγαροῦν ὁρῶσαι, ὅτι ἄλλο μὲν οὐδὲν αὐταῖς πρόσεστι, μόνον δὲ συγκοιμῶνται τοῖς ἀνδράσι, ἄρχονται καλλωπίζεσθαι καὶ ἐν τούτῳ πάσας ἔχειν τὰς ἐλπίδας. προσέχειν οὖν ἄξιον, ἵνα αἴσθωνται, διότι ἐπ᾽ οὐδενὶ ἄλλῳ τιμῶνται ἢ τῷ κόσμιαι φαίνεσθαι καὶ αἰδήμονες.

“Women, from the age of fourteen, are called 'mistresses' by men. Therefore, seeing that nothing else is available to them, but only to sleep with men, they begin to beautify themselves and, in this, they hold all their hopes. It is worthy of attention, therefore, that they recognize that they are honored by nothing other than appearing orderly and modest.”

Epictetus' Enchiridion 40 (Handbook)