Lady Croissant received mixed critical reception. AllMusic's Marisa Brown called Sia's vocal performance "rich and passionate" and made comparisons to Nelly Furtado and Morley. Brown stated the band was "tight and lush" and that the music was "very modern, warm and melodic and cleanly intricate". In his review for BBC Music, Paul Sullivan wrote that the album successfully displayed Sia's vocal capabilities and versatility. However, he noted the minimal audience participation and felt that this prevented the album from capturing a "live" experience. For Sullivan, highlights included "Don't Bring Me Down", "Destiny" and "Lentil", which he believed were "executed with an appealing mixture of frankness and fluidity". Mark Perlaki of Gigwise.com awarded the album four of five stars and opined that the album "portrays an artist who's star is in the ascendant, whose voice is unrivaled in style and expression, an artist on the brink of deserved and assured greater recognition." The Selby Times 's review called the collection "mesmerising" and a good indicator of Sia's future work. One reviewer for WERS called the album "breathtaking" and wrote positively of Sia's vocals and the instrumentation. Like Sullivan, the reviewer warned that listeners expecting a traditional live album with "raw cuts and heavy improvisation" might be disappointed.
Roque Strew of Pitchfork Media found Sia's Adelaide accent to be a "liability", specifically noting difference in pronunciation between the studio versions of "Destiny" and "Distractions" and the live performances. Strew complimented "Pictures" and "Lentil", the latter of which shined through the "fog of elongated syllables and cut consonants".Popmatters' Mike Schiller felt the instrumentation was "robotic" and found Sia's vocal manipulation and bending of vowels "infuriating", even unintelligible at times. Schiller did, however, favor her vocal tone and found the power of her voice "occasionally transcendent". Stuart McCaighy of This Is Fake DIY appreciated "Pictures" but also criticized Sia's performance for lacking diversity and for "incomprehensible" vocals due to her slurring of words. McCaighy concluded that, like other live albums, Lady Croissant was redundant but would be appreciated by fans. The Australian gay publication DNA wrote a mixed review for the album in 2010 following the release of We Are Born, complimenting Sia's vocals but accusing "Pictures" of sounding like a B-side.