A laminar jet spray diffusion flame is analyzed mathematically for the first time using an extension of classical similarity solutions for gaseous jet flames. The analysis enables a comparison to be drawn between conditions for flame stability or flame blow-out for purely gaseous flames and for spray flames. It is found that, in contrast to the Schmidt number criteria relevant to gas flames, spray-related parameters also play a critical role in determining potential flame scenarios. Excellent qualitative agreement for lift-off height is found when comparing predictions of the theory and independent experimental evidence from the literature.