"A picture just means I know where I was every minute," Andy Warhol once said. "That's why I take pictures. It's a visual diary." In this instinct, Warhol was, as always, ahead of the game. One senses that he would have been very much at home in today's digitally driven, relentlessly mediated world where diaristic photography – the recording of the everyday – is a predominant form.

Likewise William Burroughs, a writer who photographed the world around him, wherever he was, whether New York, London or Tangiers and processed the results at the nearest chemist's. Both were drawn to the disposable nature of photography but, paradoxically, took great care to arrange their images – in Burroughs's case, into meticulous collages. Warhol's embrace of photography, though, was central to his wider artistic practice, while Burroughs's use of photographs – in series, cut-outs and collages – dovetailed with many of his experiments with language and with his often opiate-driven search for different ways of seeing. Burroughs and Warhol make curious artistic bedfellows, nevertheless, even without the presence of David Lynch, whose work is entirely different. That is why The Americans Are Coming is presented not as a group exhibition, nor an examination of how photography fed into these artists' work in other media, but as three shows in which we have a chance to assess their photography in its own right. It almost works.

In this triumvirate of maverick American talents, David Lynch emerges as the most old-fashioned, that is to say, formally consistent photographer. In The Factory Photographs he is represented by his pictures of the single subject of the title – deserted industrial spaces. (He also photographs nudes and forlorn snowmen.) His black-and-white photographs of decaying buildings are really black and grey. Taken as a whole they make a kind of elegy to industrialism and, in their ominous darkness, possess a unified aesthetic that sets him apart from the other two artists.

There may be echoes of Mondrian in his geometric framing of tall windows, but the interiors, all shadows, looming machinery and snaking pipes, are utterly Lynchian, so much so that many of these places seem familiar. His early film Eraserhead (1977) is the most obvious touchstone, and one can almost hear the unnerving ambient soundtrack as one gazes at an old factory in his adopted hometown, Los Angeles.

Curator Petra Giloy-Hirtz (each of the three shows has a different curator) has arranged Lynch's prints according to location, so the mostly exterior shots of industrial spaces in East Germany and Poland give way to more intimate – if that is the right word – images of dilapidated buildings in America and Britain. In this context, the telltale cooling towers of our fading industries seem almost cosily familiar against the darkness and decay elsewhere. You enter a very defined, recognisable interior world of the imagination where the definition of beauty is peculiarly Lynchian: grey, sombre, murky, winterish. He is, as we already know, a master of atmosphere, but linger too long and you may, like me, long for some colour and breathing space.

On a separate floor, Warhol – one of the great modern colourists – is also represented solely in black-and-white, which may be one reason why the show underwhelms. There are none of the famous celebrity Polaroid portraits, though a smattering of celebrities include his friends Liza Minnelli and Jean-Michel Basquiat. She is dancing; he is eating. Both are framed in grids of stitched-together, repeated images – the artist hired seamstresses to sew the prints together. These are Warholian in their use of repetition but seem, even by his detached standards, lifeless and uninteresting. Likewise his street photographs – a newspaper stand, a manhole. The mundanity may be the point, but it seems an oddly unconvincing one.

Here and there one senses a curious, rather than deliberately blank, imagination at work: a shot of a crowd of paparazzi on a pavement awaiting a glimpse of Arnie Schwarzenegger, some of whom seem to be posing for Warhol's camera. If Warhol immediately recognised the so-called democracy of the relatively cheap point-and-shoot camera when it was used continuously and without formal rigour, his images attest to the essential meaninglessness of this approach. They signal the coming of the contemporary digital age in all its visual profligacy, while also confirming Susan Sontag's belief that "needing to have reality confirmed and experienced by photographs is an aesthetic consumerism". That idea would not have bothered him, of course, which is why he remains one of the key artists of our time: a blank observer of our empty desires.

William Burroughs looked at the world altogether differently, attuned to, among other things, conspiracy, dream logic, hallucination and Dylan's notion that "to live outside the law, you must be honest". Not the biggest fan of his writing, or indeed his world-view, I was pleasantly surprised by this fascinating selection of his photographs, pointedly called Taking Shots – a reference to his love of guns and, I surmise, shooting up. There's certainly something of the suspended, interior world of the heroin user in some of work on display here, particularly in the small-scale and meticulous arrangement of his collages, which suggest someone with time on their hands and an altered perception. Their charm is surprising, though, as is the way Burroughs tunes into, accidentally or otherwise, some of the conceptual undercurrents of the time.

In one series, What Was, What Isn't, made in London in 1972, he photographed a bed before and after he'd had sex with his sometime partner, John Brady. It's a characteristically desolate depiction of the encounter, the only suggestion of human presence the ruffled and stained sheets. The series ends with an image of the newly remade bed – order restored in the shape of a deep-red bedspread. Elsewhere, there are portraits, some taken on a Polaroid camera, of friends, lovers and fellow travellers, including Ginsberg and Kerouac, and self-portraits, in which he is often blocked or half hidden as befits a self-styled outsider and exile.

There are several examples of how Burroughs applied his famous cut-up technique to photographs, creating collages, including a surprising one of Parisian landmarks, that nod to surrealism and to his own wilfully fractured writing. More intriguing are two other series: New York Car Accident, in which he views the aftermath of a crash from different perspectives, and a group of images taken in Gibraltar. In the latter, the streets are deserted and the countryside, all pylons and glimpses of the looming rock, looks like the set of a science-fiction film in which all human life has been erased. These images are consistent with the form and subject matter of his fiction, but also work as photographic experiments in their own right.

Likewise, Burroughs's sad and austere snapshots of his hometown, St Louis, Missouri, to which he fleetingly returned in 1964, shooting deserted parks, houses and industrial buildings on a humble Zeiss Ikon camera. There is a humility and awistfulness to these images that run counter to the myth of Burroughs the unrepentant literary outlaw and loner.

More affecting still are the ephemera, which include a book on flower arranging written by his mother, Laura Lee Burroughs. The introduction begins: "Beauty is everywhere – and we have used for our decorations not only beautiful flowers but whatever we could find – weeds, vegetables, sugar cane, succulents, ice cubes, cacti, seed pods and sticks and stones. The way things are assembled is what makes them interesting." He was, then, for all his rejection of things suffocatingly bourgeois and respectable, his mother's son. This show may make you think again about the role of photography in the work of Warhol and Lynch, but it's Burroughs's images that are both the most singular and the most integrated into his other great adventure.