A "lemon" fic is an old-school fandom term for something porny/NC-17. I honestly have no idea as to the origin. I know there used to be some distinction between lemons and limes, but by the time I got to fandom circa 2002 that was falling out of favor and I never figured out the difference.
Lemon chicken fic is a particular trope where everyone else in the story is really mean to the central character, but then (usually) realize their behavior was wrong/based on a misunderstanding, and comforting apology follows. I think the origin is SGA fandom - someone who was there might be able to answer this more specifically.
Re: Fic Discussion- Burn Our Fingers and Change Our Names
Lemon chicken fic is a particular trope where everyone else in the story is really mean to the central character, but then (usually) realize their behavior was wrong/based on a misunderstanding, and comforting apology follows. I think the origin is SGA fandom - someone who was there might be able to answer this more specifically.