Last year, Suicide’s eerie 1979 song Dream Baby Dream started surfacing in all sorts of places. It soundtracked images of buildings buckling in Adam Curtis’s film HyperNormalisation, blasted through Andrea Arnold’s road-trip movie American Honey and, following Suicide frontman Alan Vega’s death in July, was resurrected live and on record by Pearl Jam, Savages and Arcade Fire’s Win Butler.

The spectre of Dream Baby Dream is haunting 2017 too, thanks to LCD Soundsystem, who open their fourth album – their first in seven years – with a phenomenal reimagining of Vega’s uncanny lullaby. Oh, Baby mimics the original’s metronomic tick and synths that dilate into pools of golden light, then leader James Murphy subs his own similarly stately, Roy Orbison-style melody. Four and a half minutes into the track, however, Murphy stops paying tribute to Vega and starts referencing another musical deity: himself.

As he evokes the climactic vocal from his 2007 single Someone Great, it’s a reminder that Murphy has never been shy about positioning himself in the orbit of his idols. This isn’t the first time he has twisted a well-known song into something that is jaw-droppingly brilliant in its own right. In 2010, he blended the riff from David Bowie’s album Heroes with the muffled guitar of Brian Eno’s Here Come the Warm Jets to create the exceptional All I Want. Neither has Murphy – the ultimate connoisseur turned auteur – been one to play down his own influence on music. “I was the first guy playing Daft Punk to the rock kids”, he boasted on Losing My Edge in 2002. (Indeed, DFA, the label he co-founded, became famous for pioneering a mix of post-punk and cutting-edge dance music.)

Farewell, but not for long … LCD Soundsystem at Madison Square Garden, New York, in 2011. Photograph: Theo Wargo/Getty Images

LCD Soundsystem’s recent hiatus, which they claimed would be permanent, was further proof that they considered themselves a Very Important Band. Their supposed farewell gig at Madison Square Garden in 2011, later bolstered by a magisterial documentary and five-vinyl box set, was engineered to amp up the critical recognition, fan frenzy and, as Murphy recently revealed, ticket sales..

In light of that, LCD’s return could appear to be yet another cash-in. Luckily, Murphy has the perfect justification for their comeback – one that, serendipitously, also boosts the band’s bid for canonical status: it was no less than Bowie who encouraged them to re-form. “I was talking about getting the band back together,” Murphy told Lauren Laverne recently. “He said, ‘Does it make you uncomfortable?’ I said ‘Yeah.’” He said, ‘Good – it should’ … David was always making himself uncomfortable.”

An unavoidable question percolates through American Dream: are LCD Soundsystem ​​also one of the greats?

It turns out Vega isn’t the only ghost haunting American Dream. The album is a swirling sea of references to Bowie. Murphy’s conversation with the late musician is referenced on Other Voices. Meanwhile, on the track I Used To, Murphy is the young fan, transfixed by his idol’s “hands in their weird positions”, yet the song sonically recalls late, lugubrious Bowie. His earlier sound is instead summoned on Change Yr Mind with sudden bursts of thin, wiry guitar.

A few years ago, Murphy was approached to co-produce Blackstar, Bowie’s final record. He declined, although he contributed percussion, and his regret provides the subject matter for Black Screen. “I had fear in the room / So I stopped turning up,” he admits, “but I should have tried more.” Occasionally, Murphy hammers home the validation Bowie gave him, walking a fine line between heartfelt elegy and giant humblebrag when he mentions Bowie’s “quick replies” to his emails.

Virtuosic and starkly beautiful, there is no doubt these Bowie-centric tracks do the late musician justice. Yet they’re not where the heart-stopping joy of American Dream lies. That is found where LCD sound most like themselves. On Tonite, for example, Murphy and his gaggle of robo-harmonisers sardonically read too much into mindless pop songs over squelching synths, while continuing his trademark meditations on ageing. (Now, he introduces himself as a “hobbled veteran” in a genuinely laugh-out-loud passage). Call the Police, meanwhile, is a sour, simmering survey of modern America that references resurfacing antisemitism and the brain-scrambling effects of online chatter while name-checking Leonard Cohen, Lou Reed and Bowie’s Berlin period. One of Murphy’s signature lump-throated vocal melodies swells throughout.

Thanks to their pored-over comeback, the allusions to Bowie and his game-changing contemporaries, and their own obviously healthy ego, an unavoidable question percolates through American Dream: are LCD Soundsystem also one of the greats? Tonite and Call the Police are as good as anything they’ve done, while Oh, Baby miraculously manages to outshine their dazzling previous work – even if not every track keeps up with this exhilarating pace. The only thing able to overshadow American Dream is LCD’s own formidable past, suggesting that, yes, in fact they are.