To be precise, Lyon was a member of the Damocratic-Republican Party.
"The Democratic-Republican Party was founded by Thomas Jefferson and James Madison around 1792. Supporters usually identified themselves as Republicans, but sometimes as Democrats." - Wikipedia
The Republican Party was not founded until 1854.
Even though it can cause confusion to those who don’t read the entire article it is right to define Lyon as a “Republican” (though not the same as today’s definition of such) vs. the other party of the time which espoused “Federalism”.
[Plus, this would probably cause a few liberals’ brains to explode so that’s just an added benefit that to me overrides any possible confusion! LOL — just joshing of course!]