“LSK” stands for Liddel, Jones and Konstantinidis. Anestis Konstantinidis was the guy who translated the lexicon into Modern Greek in 1904.
I had known that this version existed. Randall Buth had referred to it a few times, but until recently I had never seen it. I had assumed that the Modern Greek it used was sufficiently different from classical so that the lexicon would only be useful to those who knew Modern Greek. Otherwise, you would have thought that Buth and others would have promoted it as a type of monolingual Ancient Greek lexicon.
But recently Emiliano Caruso, author of the new Monolingual Dictionary of Ancient Greek, brought the LSK to my attention by locating some previews of a new edition offered by Pelekanos Press:
https://books.google.it/books?id=8HC8BwAAQBAJ&printsec=frontcover&hl=it#v=onepage&q&f=false
And this site provides a searchable version of the complete older edition:
http://myria.math.aegean.gr/lds/web/view.php
As far as I can tell, the only real difference between the two versions is the type face. I assume the older version is in the public domain.
Now, it turns out the the Greek used in LSK, far from being the sort of Demotic one finds in contemporary Greek newspapers, is extremely close to Classical-Koine. The bulk of LSJ, of course, are the citations from Ancient Authors, and these remain unchanged in LSK. The only things that need to be translated from English to Greek are the meta-language, most of which is actually composed of abbreviations, and the glosses-definitions. The abbreviations are virtually all intelligible to anyone who knows Ancient Greek: μέλλ., ἀόρ Β, Παθ., etc.
Now, to come to the heart of the matter, you can check it out yourself and come up with your own figures, but I would say that at least 80% of the time, the English definitions are rendered in a Greek that is indistinguishable from Ancient Greek, providing the intermediate student with an excellent monolingual definition of the headword. The LSK, that is, 80% of the time functions as an excellent monolingual Ancient Greek lexicon.
There are only three types of instances where the fact that LSK is in Modern rather than Ancient Greek is a problem.
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Sometimes the Modern word is the same as the Ancient word, so LSK will not give a Greek rendering but will simply say ὡς καὶ νῦν.
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Sometimes the glosses/definitions will be in a type of Modern Greek that is not comprehensible to someone who knows Ancient, but not Modern. As a practical matter, though, many of us who will wind up using the LSK have picked up quite a bit of Modern Greek, so this mitigates against the problem. Modern Greek words which are completely different than classical are put in quotation marks.
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Theoretically the LSK could use words that mean something a little different in Modern Greek than they do in Ancient, potentially causing some confusion. I haven’t seen any instances of this. It it happens it would be extremely rare.
To make use of LSK, the student of Ancient will have to learn a very limited amount of Modern to Ancient conversions: ειμαι = ειμι, ειναι = εστι, να = ινα. etc.
The value of LSK will be judged differently by those who do and do not value monolingual resources. To Grammar-Translation advocates who see no need to avoid L1, a Greek version of LSJ will seem unnecessary. To those of us who wish to avoid what Joel has caused “code switching,” or to embrace what Chad has called the “re-enforcing language loop” the LSK will be very welcome. With the LSK and Caruso, which supplement each other very well, we are about 85% towards the goal of having a complete monolingual Ancient Greek lexicon.
I’ve been using the LSK in my monolingual reading of Ajax. I am of course very familiar with using the LSJ, so I can compare the two. The advantage of the LSJ is that it is much faster to get to the meaning of the headword, and the English gloss gives you a meaning which (in a way, anyway) is more precise to someone who is more fluent in English than in Ancient Greek. The advantage of LSK over LSJ will be self-evident to those committed to the Direct Method/Immersion Approach to learning Ancient Greek.