On Tue, 23 Mar 1999, Asayogure wrote:

Very well it seems I have foot in mouth-itis this week.  The terms
[Lemon/Lime] originated from a couple of sources I am not going to get
into.  The short of it is that when you read a fic with graphically
sexual content , you tend to walk away with a sour, bitter taste in your
mouth.  Hence the citrus reference, thus Lemon became a slang term for a
strong occurrence with connotations to this regard, and finally Lime for
a weaker reference to this occurrence.  I hope I have properly removed
my foot from my mouth now...if you'll excuse me I have to go wash out
this bitter taste from my mouth... ^_~

No.

The word "lemon" comes from the series "Cream Lemon" and the manga "Lemon
People".

It is also supposedly a slang reference to genitals (which is what it is
doing in the title to begin with) but I haven't seen that confirmed.