It kind of is an oxymoron.
Hmm. You may end up having a very interesting, and possibly short, academic lifespan in political science.
PS Rule of law is critical to both a democracy and a republic.
In modern democracies, yes. But in pure democracies, it isn't. Athens is universally considered the first true democracy, and rule of law as we know it didn't exist. Yes, they had laws and yes, they had to obey them, but "The People" were not bound to them when exercising their democratic power. "The People" could vote for anything, and in effect the law was whatever they decided. In constitutional democracies the people cannot even by referendum override constitutional law (they can change the constitution, but it takes more than just a majority of the people to want to do that). In Athens, a majority of the people could change or negate *any* law. That's what is meant by rule of law operating on a democracy.
PSS. kind of a side point. Our Constitution is fairly unique in it tells the GOVERNMENT what it can and cannot do not the other way around.
Err. To the extent that I'm aware of foreign constitutions, most western democracies are governed by constitutions that both specify and limit governmental power. The US constitution was novel at the time it was drafted, but most of its concepts have been adopted by many other countries since then.
I have heard it said in some circles that the US Constitution is unique in that it vests power in the people and limits the government, whereas other western constitutions vest power in the government itself. But that's not true. It is the Declaration of Independence that claims to vest ultimate political power in the people - which was a necessity because the document was intended to justify the breakaway with England which would otherwise be treason. The US Constitution itself makes no such declaration. It does say "We the People ... do ordain and establish this Constitution" but it is worth noting historically that the US Constitution was declared to be the law of the land after only nine of the original thirteen states ratified it. And the Constitution was ratified by state legislatures, not by referendum of the people.
In fact, interesting historical note: Rhode Island was the last of the original thirteen colonies to ratify the US Constitution. It did so in May 1790. This was almost two years after the US Constitution became formally the law of the land in the United States (June 1788) and over a year after George Washington is elected President (February 1789). But most importantly, Rhode Island put the US Constitution to citizen referendum
and its citizens overwhelmingly rejected the Constitution.** The people of Rhode Island did not want to adopt the Constitution, but the Rhode Island legislature (after a lot of debate and a lot of arm twisting) eventually ratified the Constitution by a very close vote (34 to 32).
** Apparently Rhode Island citizens voted to reject the US Constitution 2708 to 237. That is over eleven to one against.