Usopp is a liar.
Apparently, Fuguko has a boyfriend who is a complete liar and they fight quite often.
In that era, all liars were to be burned.
If lies puke (吐く) out of your mouth, you're a liar.
This is a combination of the kun'yomi readings, one of which you haven't seen yet. You'll see this word without the 吐 kanji too, but for now let's learn its kanji reading!
You can't just tell one lie, it always turns into two (つ). Kind of like a chip or pretzel, you can't just have one. With lies, you have to open your mouth for two more. And then two more.... and... well you get it.