Agreed, it means 'put your lights out' or 'put you out of consciousness'. But I know why you are confused. There is an expression, used in connection with wooing. It is rather crude, but it means that the girl who is being pursued would allow the male to have sex with her. She would 'put out'. It is very similar to this expression, but it is an impolite expression, you should not expect to hear it except from impolite males (perhaps in movies, or books etc)

It sounds they are living together and don't have sex with each other, of course, they are brothers, so put him outside, outdoor, so maybe meet some female and have some sex.... Don't think too much...

This is where you need to be careful with phrasal verbs. If you say "someone puts out", with no other person or object, then that person will offer sex, usually in exchange for a favour. It's a pretty rude thing to say about anyone, so don't use it. If you want to add a "recipient", then the pattern is "to put out for (someone)". "To put (someone) out" is in your example, and the meaning is found only from the context. They're talking about getting sleep, so "it'll put you right out" clearly means you'll sleep soundly. "Out like a light." A different context could change the meaning to "disappointed", "inconvenienced", "outside", "out-of-place (eg. "dislocated")", "offered", "rejected" and so on... So you need the phrasal verb, the pattern AND the context to get your meaning. That's how we know it naturally.

No, in a word. It means 'put you to sleep'. He could have meant masturbate, but more likely 'real' sex. BTW:There are two middle-aged men and they're brothers. The younger brother couldn't sleep, the older one suggested that he take a pill or drug himself. But the young one refused and hoped to have an all-natural sleep.[1] Then the old one said: "Okay, in that case I do know a great all-natural sleep aid, you should get yourself some sex, It'll put you right out." [1] or 'do it an all...'

There is nothing in your story to indicate that the old one is particularly suggesting masturbation. For all we know, he is suggesting that his brother go visit his girlfriend. But, since masturbation is a form of sex, I suppose "it'll put you right out" too.