Whether or not a business or organization is an LLC doesn’t really determine whether it has to pay taxes. Whether it’s owned by a citizen or not doesn’t either.
First, consider what you mean by citizen. Title 26 has a different definition of citizen than the rest of the US code. According to immigration and criminal codes, the definition is nearly identical to what’s written in the constitution. (Born in the US or naturalized, etc). When dealing with taxes in title 26, some believe that citizenship and residency are limited to Washington DC by the definition of United States. Some courts have disputed this.
But even if you are a resident or citizen of Washington DC, the LLC or Corporation does not necessarily have to pay taxes. You might, if you receive money from the organization or sell it. If it is a “single member LLC”, the IRS treats it as if it doesn’t exist. The LLC will not file, but the owner will.
To determine whether either LLC or owner or even a Corporation has to pay taxes, you have to consider the source of income, which is the same as an individual. There are different reasons it might receive taxable income. Some of the obvious won’t apply. A business would never receive wages or be elected to a public office. But if it has a government contract, that might qualify as taxable income. The same rules will apply. If the business has taxable income, it’s required to make a return or statement.