For the origin of this quote, see The Simpsons episode "Simpson Safari". The use is truly ironic, because the term was used to described something of mind blowing unlikeliness. However, I have come to use it to describe something that everybody knows is going to happen, but is still surprised. Today, someone tried to tell me it is ironic that a person who eats cheeseburgers every day eventually has a heart attack. That's not ironic, that causality.
This term has come to describe a number of statistical phenomena, including selection bias, where people misinterpret the world around them. Take Alanis Morisette's man who was afraid to fly, and when he finally did, he died in a plane crash. This is a crazy coincidence, right? Actually, this is bound to happen.
Say 1 in 25 people is afraid to fly, and 1 out of 10 people on a plane are on their first trip. Add to that that a person who is afraid to fly is 5 times more likely to come with an alternative to flying, and ignoring small aircraft, the average plane holds 150 people. 25 * 10 * 5 / 150 = 5, so there should be a person who is afraid to fly on their first ever trip once out of every 5 plane crashes! Obviously a specific person crashing their first time up is rare, but so is that person winning the lottery! Given a large enough population, it would be absurdly unlikely for their to be coincidences. Therefore, the man dying in the song is not ironic, it's bound to happen.
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Wouldn't the man afraid to fly who dies on his first flight be ironic each time, despite the statistical inevitability, even if it happens a number of times?
Winning the lottery is very unlikely, but still bound to happen. It's not ironic though unless there's some kind of.... ironic element (I'm good at making sophisticated arguments....). Would it not be ironic if the lottery was won by someone who couldn't count? Which also must be bound to happen.
The question is essentially what you consider to be ironic. Does something that is going to happen given enough data points constitute irony? I don't think it does. At that point, anybody who wins the lottery is ironically winning, and by that logic, every hand of cards is ironic, every combination of traffic lights on the way to work, the order of the songs that my iPod shuffle plays. Randomness is a fundamental, if easily misunderstand fact of life. Creationists are notorious for any lack of knowledge, but you sit in a room of poker players, who all think that they're "due" for a big hand, and even intelligent mathematically minded people make the same error.
The aspect that people like to touch on for irony, is as you suggest, the buffoon who doesn't know better, and somehow lucks into winning. You know, the idiot who hits on 19 and picks up a deuce, the guy who plays the lottery every week. I don't think anyone would think the former is ironic, and what is the difference between that and the latter?
Fundamentally, it is more polite to say "ironic" than it is to say "the idiot got lucky", even though that's what everyone is thinking.
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