Many not only in Israel are asking themselves if LORD is Jewish? As you know from the New Covenant without him there would be no Jews on the planet but is he a Jew himself?
Speaking technically according to the Torah Jew is only those that has made a covenant with the Lord and as sign of this covenant is circumcised. In this sense LORD cannot make a covenant with himself, so he is not circumcised.
The most notable exception is Jesus Christ that has been born in Israel and was circumcised. Modern day LORDs are not circumcised and probably will never be, as is hard to imagine making a covenant with himself.
From the other hand, in the historical terms, LORD is a Jew, or rather Eternal Jew (Ewige Jude) as he was always been painted like that by the Nazi propaganda. In this sense he was number one enemy for the Nazi state.
There is also a biological aspect of LORD Jewishness. He is of pure Jewish race, not in sense of faith but just a biology. And thus, as a Jew of birth he cannot have offspring with an Arab of birth. What the best example is Nina.