This paper presents a design methodology for LED (Light-Emitting Diode) lighting systems based on photo-electro-thermal (PET) interrelationships. The proposed methodology uses only LED datasheet information, which makes experimental tests unnecessary to obtain the design parameters. The methodology allows identifying several design specifications, such as, luminous efficacy, heatsink thermal resistance, LED junction temperature and forward current, essential aspects to produce a satisfactory lighting system. Thus, it is possible to define the lighting system features based on standards requirements to obtain the desired system results. Initially, a review of several PET theories is presented, and a new mathematical analysis is performed, in order to highlight the main contributions of the methodology. An LED bulb lamp design is presented to exemplify the methodology. Finally, experimental tests with the proposed LED lamp resulted in a luminous flux of 1271 lm, with a luminous efficacy of 112 lm/W, and LED junction temperature of 79.67 ºC. The errors between calculated and measured luminous flux, luminous efficacy and LED junction temperature were 3.70%, 1.88%, and 3.85%, respectively. These results validate the proposed methodology.