One editor-independent approach would be to save the quotes into a separate file. You could do this in a single quotes.tex file, which might contain
\newcommand*\getquote[1]{\csname quote#1\endcsname}
\expandafter\def\csname quote1\endcsname
{%
Some American text about color!%
}
\expandafter\def\csname quote2\endcsname
{%
Another quote about neighbors.%
}
...
You could then have \input{quotes} in your main preamble, and call quotes by doing \getquote{1}, etc. (I've defined the quotes with numbers as that seemed easiest, but you might want to give them names instead.)
Now, I don't know how long your quotes are, how many there are, and so on. So this approach might not be practical. However, it is hopefully a start.
Thanks Scott! Your answer about changing the Hunspell path in Tools > Preferences > Paths worked for me. I pointed the path to
"C:\Program Files (x86)\MiKTeX 2.9\hunspell\dicts"
Lastly, had to restart Lyx and the spell checking started working.
I tried pointing it to the dict files in the Lyx resources directory ("C:\Program Files (x86)\LyX 2.1\Resources\dicts"), but that didn't work. Mine was a clean install of Lyx 2.1.4 on Windows 10.
Scott, since you're working in the Lyx project, I think you should have them set the default Hunspell path on the Windows install to the correct one, instead of leaving it blank. I just clean installed it a few days ago, so I don't think I touched any of the settings to affect this.
Also note that at least for me, the dict files in the MikTex directory were a few years old, as opposed to the ones in the Lyx resources directory which were much newer.
(Sorry I'm replying this as an answer, but I just joined and I don't have enough reputation to comment.)
Best Answer
Click on "Abc" with the wavy underline, or go to Tools > Preferences > Language Settings > Spellchecker and check the box for "Spellcheck continuously".