Earlier this month, US label Light in the Attic found itself in the curious position of simultaneously announcing they had finally tracked down the mysterious singer-songwriter Lewis and denying that they'd made the mysterious singer-songwriter Lewis up. The label's co-founder Matt Sullivan wrote about chancing upon Lewis outside a coffee shop in Canada; previously, neither the efforts of a private detective nor the news that his privately released 1983 album L'Amour had been rescued from obscurity and reissued to vast critical acclaim could bring him out of the woodwork. Sullivan then struck a plaintive note. "We are aware of the small percentage of people that believe this whole thing to be a hoax," wrote Sullivan. "Looking at the 12-year history of our label, anyone would see that we would never do such a thing to betray people's trust."

You take his point. Light in the Attic is a hugely respected label, its reputation built on meticulously curating music from the outer reaches: why damage that reputation by perpetuating a hoax on precisely the kind of record buyers who support their efforts? Certainly not for financial gain: for all the critical acclaim, sales of L'Amour are hardly the stuff to make Ed Sheeran cast a panicky look over his shoulder. And yet, you can also see why people think the story of Lewis is too good to be true. A mysterious blond playboy called Randy Wulff arrives at an LA studio favoured by hardcore punk bands, in a white convertible Mercedes, and records an album of eerie, ethereal, country-folk before apparently vanishing off the face of the earth; said album is rediscovered 30 years later, when its indecipherable vocals and billowing synthesisers chime with prevalent alt-rock trends so perfectly that one reviewer calls it the best album of 2014.

There's an argument that the story around Lewis is almost besides the point. Had L'Amour been released by a new artist on a hip US indie label like Jagjaguar or Paw Tracks, it would still have provoked acclaim. But while it's true that L'Amour would be a fantastic album whoever made it, at least part of its appeal came from the glaring disparity between the person on the sleeve and the music it contains. You somehow wouldn't expect a chiseled blonde playboy – who stories claim was either a stock market trader, a drug dealer, a con man or a relation of the heiress and philanthropist Doris Duke – to make music that sounded so introverted and fragile.

That's even more true of its follow-up, recorded in Calgary in 1985 and rediscovered shortly after L'Amour's re-release. On the cover, Lewis poses with his Mercedes and a private jet, tanned, immaculately white-suited, cigarillo in hand: he makes Bryan Ferry look like Stig of the Dump. He seems to have grown a surname, Baloue. There may be a certain boggling disbelief at the fact that a a man who was already called Randy Wulff somehow came to the conclusion that he needed a more striking name, but nevertheless, it all looks like the epitome of bombastic, alpha-male, Miami Vice-era success. But inside, as the sleeve notes point out, the music strongly suggests "something has gone wrong".

The acoustic guitar and piano are largely absent, replaced by synthesisers and a drum machine. The former variously provides clouds of ghostly ambience, cheesy lounge-act accompaniments and, on So Be in Love With Me, a grinding, bleak pulse; the latter seems to be perpetually trotting out a factory-preset rhythm. A few minutes into the opening track – a bizarre, warped cover of Strangers in the Night, retitled We Danced All Night – a saxophone saunters into view. The songwriting is every bit as alluringly idiosyncratic as that on L'Amour. Filled with unexpected melodic twists and hypnotic repetitions, the songs once again pull you into their world, but it's a place that seems far darker and more unsettling than L'Amour's realm of stoned, small-hours melancholy. Wulff's vocals have changed from a recumbent mumble to a prominent, agonized quaver. The lyrics are exactly what you'd expect from songs called things like So Be in Love With Me and Bringing You a Rose, but Wulff's voice invariably undercuts them: they sound pained, disturbing and desperate. While L'Amour invited comparison with John Martyn at his most slurred and introverted, or Arthur Russell, Romantic Times seems to exist – emotionally at least – in a lineage of music that includes Big Star's Sister Lovers, Neil Young's Tonight's the Night and Brian Wilson's contributions to the Beach Boys' Surf's Up: it sounds – harrowingly, grippingly – like someone falling apart before your very ears.

The solitary memory the engineer who worked on Romantic Times could dredge up was that Wulff appeared to be "under the influence" while making it, and it's tempting to view it as a deliberate attempt to evoke the substance-fuelled darkness lurking beneath the lifestyle depicted on its sleeve. Then again, there's always the chance that – as often happens in the world of the private pressing and outsider music – the album's effect is at odds with its maker's intention: that the title was meant unironically, that in some addled state, Wulff genuinely thought that the sound of Bon Voyage or Don't Stop It Now was seductive rather than unsettling.

Either way, he isn't saying. When Light in the Attic finally found Randy Wulff, he apparently declined a copy of the reissued Lewis CD, or indeed the royalties the label owed him, claiming he wasn't interested in the past. So the mystery remains intact: the only thing that seems certain about Lewis is how striking and unique his music was.