James Murphy is the kind of person who knows a little bit about a lot of vaguely connected subjects – making music, selling music, fashion, drugs, electronics, mixed martial arts. But the thing he understands most is the unifying concept of cool. He's spent an inordinate chunk of his life thinking about what being cool signifies, and it's something his band LCD Soundsystem dissect and reconfigure in almost every song they produce. This May, LCD will release their third (and last album), This Is Happening. And what seems to be "happening" is that Murphy has reached the apex of his (mostly real) persona; he now understands coolness so intimately that it's become an almost academic pursuit. He thinks about it more than he feels it.

"I was a lot cooler 10 years ago," Murphy says at a restaurant near his home in the Brooklyn neighbourhood of Williamsburg, North America's hipster utopia. He immediately explains the difference between being in LCD now and his early days with Death From Above, the record label he helped create in 2001 with two like-minded associates. "New York likes art stars. When I was in DFA, we were seen as these crazy guys throwing these drug parties connected to some fashion show. That was cool to people. Now I'm just a guy in a band. I suppose what happened is that I spent my whole life wanting to be cool, but eventually came to recognise the mechanism of how coolness works. So it's not really that I don't want to be cool any more – it's more like I've come to realise that coolness doesn't exist the way I once assumed."

People always mention how Murphy doesn't look like a conventional pop star, but he doesn't look like a conventional 40-year-old adult; he's 6ft 1in with a XXL torso, and his bangs protrude forward like the shelf of a cliff. His hands are enormous and he (somehow) always seems to have exactly two days' growth on his jowls. He wears a designer Yves Saint Laurent T-shirt to our interview, and he's still wearing it when he performs in front of 1,400 dance-punk nerds 12 hours later. Much like his lyrics, Murphy's conversation style toggles between low and high culture. He brings up arcane philosophies, undercuts his own ideas through self-deprecation, and then tries to reconcile the middle ground between them. Even when he talks about other people, it sounds like self-analysis.

"There are some people who are just plain great at making music. That's not who I am," he says. "However, I can succeed at making music that works as dumb body music, but that can also meet someone in the middle if they want to investigate our songs in a deeper way. I know the things I can do: I understand music and I trust my taste. And taste is important." What this essentially means is that LCD try to make sophisticated music within the simplest possible parameters. Some might call such a goal pretentious; if they did, Murphy would not mind.

"I actually want to write a treatise in defence of pretension," he says. "I think the word pretension has become like the word ironic – just this catch–all term to distance people from interesting experiences and cultural engagement and possible embarrassment. Pretension can lead to other things. You know, the first time I read Gravity's Rainbow, I did so because I thought it would make me seem cool. That was my original motivation. But now I've read it six times, and I find it hilarious and great and I understand it. You can't be afraid to embarrass yourself sometimes."

Because his lyrics are often sardonic (the new single is titled Drunk Girls) and because Murphy has a reputation for living hard (he often swigs a concoction of whisky and champagne on stage), LCD appeal to a lot of people who just want to get stoned and jump in place. But the real reason it works is because Murphy understands the nature of sound; he uses repetition and tempo to dictate how the listener emotively responds to his work. I ask him if he can remember the first specific sound that moved him.

'I used to lie on the kitchen floor and put my head next to the refrigerator vent and sing these weird melodies in my mind'

James Murphy

"Oh, yeah. Revolver, when I was six," he says immediately. "It was the song Tomorrow Never Knows. The hum on that song. The other sound that really affected me was the hum from our refrigerator. I used to lie on the kitchen floor and put my head next to the refrigerator vent and sing these weird melodies in my mind. I've always sung to machines."

Twenty-five years on, he heard that hum again – but this time he was on ecstasy. And in many ways, that was the embryonic moment when LCD Soundsystem was born.

"I was at a club not dancing, because I didn't dance. For years, I never danced," Murphy says. "I was on ecstasy and I was peaking, and then the DJ played Tomorrow Never Knows and I lost my marbles. But I also had a very important revelation, which was that the way I was feeling was actually me. It wasn't the drug. It was me. But you know, I never took ecstasy until I was 30. That's important. When it comes to drugs, I'm a big proponent of the boat-sails-wind analogy: your life is a boat, the sails are your emotions, and drugs are the wind. When you're a kid, your boat is small and your sail is huge, and drugs are like a hurricane. So you need to get to a point in life where you have a big enough boat to navigate the weather."

It shouldn't be difficult to imagine Murphy as a teenager, but it is. When he describes the younger version of himself, he sounds like a person who only exists in unrealistic teen movies – an idealistic counter-culture badass who listened to krautrock while kick-boxing. Yet when he tells these stories, the details are so rich and oblique that they must be at least partially true. Within the world of his rural New Jersey high school, Murphy was a very interesting, periodically terrifying kid.

"I used to get in fights a lot in high school," he says. "I was sort of fixated on fairness when I was 15, and I sort of looked wussy – I wore a lot of Smiths shirts and I had skater bangs. But I would often get into fights whenever things seemed unfair, and I was notorious for being a really, really crazy fighter. I hurt a few kids pretty bad. I broke one kid's orbital bone. I broke one person's arm. Broke some ribs. I was the kind of person who would sit on a guy's chest and just keep hitting him. I just got very upset any time someone would antagonise me to the point of fighting, and I wanted to teach them a lesson. I kind of got psychotic, actually."

'My dad said: The world is insanely unfair, and 99.9% of the time it's unfair in your favour. You've actively marginalised yourself'

James Murphy

The inherent ambiguity of fairness is still present in a lot of Murphy's music. On the 2007 song New York, I Love You But You're Bringing Me Down, he fixates on the phrase "Maybe I'm wrong and maybe you're right". On a new track Pow Pow, he keeps reconstructing and rewording the sentiment, "From this position, I can see both sides. There's advantages to each." Some of this obsession may have been inherited from Murphy's (now deceased) father. When he was 18, James got hassled by a police officer. Murphy's dad responded to this by saying, "Well, what do you expect? Look at how you're dressed." James countered that such a stereotype was "unfair".

His father was not sympathetic to his plight.

"You're not even Irish. You're just white," the elder Murphy told him. "Fairness only matters when you're in a position of power and you're trying to make things fair for someone else. Life is not fair. You're a white, upper-middle class male in the United States of America. The world is insanely unfair, and 99.9% of the time it's unfair in your favour. You've actively marginalised yourself, and that's your choice. I respect that. But tomorrow, you can cut your hair and become like everybody else. Try being black."

Murphy later attended New York University (he got mostly A grades). In another weird example of fairness (or the lack thereof), Murphy almost became a writer for a television sitcom in 1992. A friend had submitted Murphy's prose writing to a TV executive who was looking for someone who understood New York. Murphy passed on the opportunity; he absent-mindedly thought the offer had come from someone involved with It's Garry Shandling's Show, a comedy that ran on the fledgling Fox network from 1986 to 1990. A decade later – while looking through storage boxes in his parents' home after they'd both died – he found the old business correspondence from that period of his life. The show he had actually been offered a writing job on was Seinfeld, which would become the most popular sitcom in US history.

"I didn't think much about it at the time. I was 22. I just went back to New York to smoke pot and play guitar," he says. "But even knowing what I know now, I'm happy I didn't do it."

Recorded in drug-friendly Los Angeles, This Is Happening is very much in the vein of LCD's previous work: long, euphoric, rhythm-conscious songs that are only slightly more funny than depressing. Murphy writes exceptionally well about friendship and self-identity, and he deftly captures the aphoristic interior monologues of smart, problematic people (on the album's first cut, he sings about a person who finds himself, "Talking like a jerk/ Except you are an actual jerk/ And living proof that sometimes friends are mean"). This was a central reason director Noah Baumbach tapped Murphy to score Greenberg, a film about a former musician who loathes the world almost as much as he loathes himself. Of course, the clearest illustration of LCD's identity will always be 2002's multi-dimensional Losing My Edge.

"To me, Losing My Edge was the perfect narrative song that could have ever come from me," Murphy explains. "Everything had a layer behind it. Was it making fun of other people? Sure. Was it making fun of myself for making fun of other people? Sure. But it was also about me kind of believing the things I was saying, and it was also about being a little embarrassed for being the kind of person who would believe those kinds of things."

But now, the "kind of person who would believe those kinds of things" is (apparently) going to stop being that person; Murphy says This Is Happening will be the final LCD album (he'll still make music, but not with this same band and not in this same way). To some, the timing of this seems strange. But not to the man making the decision. He is still losing his edge, but this time it's on purpose.

"It seems simple to me," he says. "It just feels like this should be the last one. For one thing, I always told myself I wouldn't do LCD past the age of 40. For another thing, I don't know if EMI would put another record out by us. They've been very good to me and they've never tried to force me to create a hit, and everything people have told me about signing with a major label has proven untrue. But the way the industry is going, EMI might not even exist in three years. And a third factor is that I really want to do a good job, and I want to do everything myself. Now, I could have other people do some of those things for me, but then it's not really the band I want. The only reason I would do that is because this is a business, and that's not a good enough reason … It seems like something I didn't want to have happen did happen: I see this band as pure evidence that having a decent idea is more important than being talented."