The U.S. has elements of both a republic and a democracy. The definition of democracy has changed over time.
Lee's claim was misleading. While it is true that there was ambiguity over the idea of a "pure" democracy among the American founders, the intention was always to create a state with majority rule, as noted in the Atlantic.
Our modern understanding of the word democracy is different from the time of the writing of the constitution. The American founders understood democracy by its original Greek definition, which meant the direct rule of the people, and therefore not subject to the law of the constitution.
Some argue the U.S. is often categorized as a democracy when a "constitutional federal republic" would be a more accurate description.
Founding father James Madison wrote in Federalist 14: “In a democracy, the people meet and exercise the government in person; in a republic, they assemble and administer it by their representatives and agents. A democracy, consequently, will be confined to a small spot. A republic may be extended over a large region.”
The founders believed democracy to be purely run by the people, whereas a republic required representation.
It is still difficult to know if the U.S. should be categorized as a democracy or a republic. Dana Goldstein reported on the difficulty of defining these terms in the U.S. school system. "A democracy is government by the people, who may rule either directly or indirectly, through elected representatives. A republic is a form of government in which the people’s elected representatives make decisions," she writes.
“Some of the country’s political processes, like ballot referendums, are more democratic than others, like the Electoral College. Grappling with that complexity is key to understanding the American government, according to social studies experts."
The term "democracy" is not specified in the Declaration of Independence, nor in the Constitution. The U.S. still has democratic processes in place. Stating that the U.S. is definitively not a democracy is misleading.