Is there any identifiable morphology for ἔνι?
That was an interesting question. I googled ἔνι and ἔνειμι and a discussion came up in google books from "Man and Woman, One in Christ by Philip Barton Payne: “Although grammarians generally agree on how ἔνι functions and that it is equivalent to ἔνεστι, there are two reasonable explanations of its etymology. Most of the ancient grammarians regarded it as a contracted form of ἔνεστι from the verb ἔνειμι, “to be in.” This contracted form occurs frequently in classical, Hellenistic, medieval, and modern Greek. But most recent commentators follow George Benedict Winer’s analysis and regard ἔνι to be derived from a poetic form of the preposition ἐν (“in”) used in Epic and Attic Greek and in Ionic prose, ἐνί, “strengthened by a more vigorous accent” with the substantive verb “to be” omitted by ellipsis. Analogously, ἔπι (from ἐπί), πάρα (from παρά), ἄνα (from ἀνά) and μέτα (from μετά) were used with the force of ἔπεστι, πάρεστι, ἄνεστι, and μέτεστι. Either explanation of the origin of ἔνι is plausible. Since “to be” is understood elliptically in the second, both explanations result in the same meaning…”
The LSJ (1940) entries for ἀνά/ἄνειμι/ἔπειμι/μέτειμι don’t mention this phenomenon.
What is “K” in this context.
(This usage is not mentioned under περίειμι)
That’s a rare slipup for LSJ, but uppercase Greek letters refer to books of the Iliad (though LSJ does not use that convention!), and lowercase Greek letters to books of the Odyssey. Κ means book 10 of the Iliad, and Iliad 10.244 does indeed read: οὗ πέρι μὲν πρόφρων κραδίη καὶ θυμὸς ἀγήνωρ
By way of a corrigendum, I mis-referenced the lexicon entry there. That is actually from Georg Autenrieth, A Homeric Dictionary. Apologies especially to opoudjis.