When fish die, bacteria begin working to liberate amines from the amino acids in the fish's flesh.
An Amine is basically a hydrocarbon attached to an NH2 group (derived from ammonia). Like ammonia, amines are weak bases in water. Most amines are very pungent, and are the source of many of the "rotting" odors we know. In fact, some of the amines in fish are known (scientifically!) as cadaverine (C5 H14 N 2 , produced by the breakdown of lysine), and putriscine (C4 H12 N 2 , which is produced by the breakdown of glutamine).
Since amines are basic, mixing them with an acid results in the formation of an amine salt. And this is where the lemon juice comes in.
Everyone is familiar with the sour taste of a lemon; this taste comes from citric acid (which contains three carboxylic acid groups). When we squeeze that lemon wedge onto our fish platters, we are setting up a reaction that neutralizes the fishy-smelling amines, thus greatly improving the taste of the fish.
Memorize this explanation and use it to impress your date when dining out at an expensive restaurant. Just remember whom to thank when members of the sex which you prefer are beating down your door...