It's quite straightforward with some nice repetition, and I think it will be my text for a baptism sermon in a month or so.
A Opening (love in truth, loving the truth) 1-3
B Walk this way (in the truth, in obedience, in love) 4-6
B` Don't walk away (those who run ahead, beware of deceivers) 7-11
A` Closing (this is the start, the goal is completing the joy) 12-13
"truth" occurs four times in the first three verses, and then again in the three-fold description of how we should walk (in truth, in obedience, and in love). The "walk" metaphor is changed into "running", for those who run ahead, and essentially run away from the truth. The message is one should not walk with them (cf. Ps 1:1) because that would be to share in their wicked work. The conclusion, which echoes language of the opening, explains the goal of this letter and the "elder's" interaction with the "lady", but could be extrapolated to the goal of walking in the truth and not in the way of wickedness, which is to complete one's joy (cf. 1 Jn 1:4).
I still haven't worked out what to say about the identities of the characters (the lady, her children; the sister, her children), but it is nice to see the word for "lady" is κυρία, that is, the feminine version of κύριος (Lord), which might point in the direction of the bride of Christ language.
It's a brief letter, but lots in it. A nice ABBA structure never goes astray either.