There are two sorts of lights one can put out.
One is their "vital spark", that which differs the living from the dead. Hence in the following quotes about putting out someone's lights, it means to kill them:
But once put out thine, I know not where is that promethian heate, That can thy light returne. — Shakespeare, "Othello".
Quench thou his light, Destruction dark! — Walter Scott, "Lady of Lake"
Put his lights out, to kill — A. J. Pollock, Underworld Speaks (a lexicon of criminal slang in 1930s America).
The other is the power of sight, or by extension, in the plural, ones eyes. (The OED describes the use for eyes as "now slang"):
Lift vp thine eyes..They were not borne to loose their light so soone. — G. Wilkins Miseries Inforst Mariage
His ministers with point of piercing sword Put out my light for ever. — R. W. Dixon Mano
To punch someone's lights out, is hence to render them (perhaps permanently, but most often temporarily) unable to see by reason of being unconscious or at least greatly stunned.
But the other definition I give above, with the more violent meaning of killing someone, is worth considering too, as a likely influence.
As a slang expression, it's not necessarily one or the other in terms of literal meaning, and figuratively can be much looser again. The threat "I'm going to punch your lights out" can perhaps be interpreted as "I'm going to render a considerable amount of violence upon you, probably with my fists, which will result in a not very well-defined, but certainly considerable, degree of injury". It doesn't need to be clear as to which of the two possible literal meanings it relates to.
(It's possible that Pollock's phrase actually belongs with the second meaning of lights rather than the first, and they misinterpreted. Certainly their definition of bananas as meaning sexually perverted has little supporting evidence and it could be that they were not as fluent in underworld slang as they thought they were. Note that this was, for a time, the FBI's manual on the topic!)
The definition of lights you have found tends not to be used any more of humans. Indeed, the definition you give has it not even used much of food for humans, which seems sad to me (pluck, which is lights mixed up with heart and liver is of course the key ingredient in haggis, and absolutely delicious). The word is derived from the adjective light in the sense of not heavy, and was once more often used of people, including the pleonasm "lunges and lightes" from Spenser's Faerie Queene.
There is a colloquialism whereby one scares someone so greatly as to remove the lights, and sometimes the liver, out of them:
It most scared the livers and lights out of me. — Twain, Adventures Huckleberry Finn.
You might start by questioning Likhas, scare the lights out of him, and he might tell you. — Pound, translation of Sophocles "Women of Trachis".