No, in fact they descend from the accusative forms, lēgem and rēgem. I don’t know much about the precise evolution, but g → y strikes me as a perfectly normal sound change, especially before /e/. Looks like it happened in the other Romance languages too: compare French roi, Portuguese rei, Italian re, etc.
In that case, German switched to "t", not English from. High German is the main odd one out of the Germanic languages in this case.
Compare "Dag" (low German)"; Saterland Frisian "Dai"; West Frisian "dei"; "dag" in Old Saxon, Dutch, Norwegian, Swedish, Danish); Faroese and Icelandic "dagur"; Gothic "dags"
d -> t is one of the major High German consonant shifts. Other examples of the d -> t shift is Vater vs. vader, fader, father (from Middle English "fader", so there the "th" in modern English is also not from the German)
Others prominent changes around the same time included e.g. p -> ff (Schiff vs. ship, schip, ship, skip, skib in other Germanic languages) and /t/ -> /t:s/ etc. - compare Zwei with two, to, två in other Germanic languages.
Very few of those changes made it into English, either Old English at the time, or later - English in that respect tends to be closer to Low German than to current standard German.
(as an English speaker - or a speaker of basically any other Germanic language -, to learn German having a rough idea about the consonant shift is a major help in figuring out German vocabulary - you'll find a lot more German words are "close enough" to be understandable once you recognise the changed sounds)
If focused on that, because the consonant shift is generally what shows us which words come from German vs. Germanic, rather than address the subsequent shift from g.
The softening of the "g" into "y", "j","i" is also a feature in other Germanic languages for many other words. E.g. in modern Norwegian "deg" (the object form of "you" / "thee" which is necessary in Norwegian still) can be pronounced both with a very pronounced g, and with a tiny shift of the tongue to soften it into a i/j. In English we have "dough" where the "g" has disappeared, but was still there in Old English, and where in modern Norwegian you again can choose /dɛɪːɡ/ or /dæɪ̯/. They all, again, share a root in Germanic with the German, where we again have a strong indication the other Germanic languages evolved their current versions from Germanic rather than German in that the German got a "t" from the consonant shift: "Teig" (vs Low German "Deeg")
Jepp, that's precis som på svenska, där “dig” uttalas “dej”. But AIUI you can see from old songs and poems, by which words it was used to rhyme with, that the spelling is how it used to be pronounced not so many centuries ago. (And yes, “dough" heter “deg” på svenska också. Så og på norsk, antar jag?)
correction: spanish is heavily ablative case instead of accusative. original statement is correct in principle since lex, rex are nominative and first in a nominative-genetive form in latin dictionaries. eg. lex, legis. rex, regis.
No, in fact they descend from the accusative forms, lēgem and rēgem. I don’t know much about the precise evolution, but g → y strikes me as a perfectly normal sound change, especially before /e/. Looks like it happened in the other Romance languages too: compare French roi, Portuguese rei, Italian re, etc.