LP1 received mixed reviews from music critics. At Metacritic, which assigns a weighted mean rating out of 100 to reviews from mainstream critics, the album received an average score of 59, based on 18 reviews, which indicates "mixed or average reviews".Jon Pareles wrote for The New York Times that "[f]or most of the album she lets her big, smoky voice rip into songs of all-out romantic strife" and that "[h]er voice is a loose cannon; LP1 figures out how to aim it."The Boston Globe's Scott McLennan noted that the album "has bolder blues-rock and country undertones, and those platforms elevate the originality of Stone's raw talents." He further stated: "With her rich tone that is cut with a bit of rasp, Stone has the ability to inhabit songs the way good actors create characters."Stephen Thomas Erlewine of AllMusic stated that "Stewart is naturally reluctant to present Stone in a strictly soul setting; R&B is the foundation, but he dabbles in tight funk, folk, blues, Euro-rock, and modernist pop, giving LP1 just enough elasticity so it breathes and just enough color so it doesn't seem staid." Holly Gleason of Paste described the album as "a full-tumble of relentless musicianship, grit and soul" and compared it to Dusty Springfield's 1969 album Dusty in Memphis. She later concluded that "[i]n a world where machined dance fodder, rap-deckled pop and lumbering rawk dominates, a genuine article of soul music—especially one where the thick bass, tumbling Wurlitzer and bright guitars set the tone—is a joyous noise, indeed."The Guardian's Paul MacInnes believed that the album is "proficiently played and Stone's voice has a range and tonal dexterity that few of her peers possess", but "the final product is so familiar and so shorn of genuine emotion that LP1 quickly loses any sense of identity and becomes standard fare, indistinguishable from any number of other recordings." Colin McGuire agreed in his review for PopMatters, and said that the album is "missing the key element of why she has been so lauded over the course of her increasingly mature career: A groove. In fact, [LP1] lacks so much of a groove, it would be safe to say the singer has almost completely abandoned her soulful roots altogether", deeming the result "disappointing", "low-rent", "unexpected" and "most of all, it seems like something Joss Stone was previously above".
Mike Diver from BBC Music claimed that LP1 is "no successor to The Soul Sessions. It's too loose, too unkempt to promote its maker back up to pop's uppermost leagues. Stone packs all the power you expect, but her control misfires enough for some of these tracks to never quite click as they might." He nevertheless referred to Stone as one of the UK's "most gifted singers, and when she shines the effect is positively blinding."Rolling Stone critic Caryn Ganz commented that "Stone is best when she's rawest, bookending LP1 with 'Newborn' and 'Take Good Care,' stripped-down tunes where her howl goes from plaintive to bone-shaking in a few lovesick heartbeats." Andy Gill of The Independent remarked that the album is "less hostage to a single specific style than any of her previous work" and that "the diversity emphasises her shared heritage with Janis Joplin, while retaining her core deep-soul strength on tracks such as 'Cry Myself to Sleep' and 'Newborn'." Matthew Cole from Slant Magazine felt that "sameness is [...] an issue [for the album], as most of the songs here aspire to little more than providing scenery for Stone's vocals." He continued: "This a wholly acceptable effort, but it makes it clear that Stone is stalling out a mere decade into what looked at first like a promising career." Mikael Wood of the Los Angeles Times viewed it as "Stone's most conventional record yet" and opined that "the music gestures toward the majestic balladry we've heard a lot of lately from Ryan Tedder in his productions for Beyoncé and Kelly Clarkson. But such a mild reward hardly seems worth the trouble of her protracted freedom fight." Kenny Herzog from The A.V. Club was emphatic, dubbing it Stone's "flattest and phoniest album yet" and "an almost shockingly forgettable slab of forced adult-contemporaryrock", adding that "[d]espite a capable vocal range, Stone primarily dials up screechy wails [...] and contrived, finger-wagging sass." Joanne Huffa from Now argued that "[d]ated production could be overlooked if the songs were better, but there's a serious lack of hooks for a pop album. And since Stone's voice is the focal point, there's no escaping the leaden lyrics."