There has been considerable interest in inorganic scintillators based on lutetium due to their favorable physical properties. Despite their advantages, lutetium-based scintillators could face issues because of the natural occurring radioisotope of ¹⁷⁶Lu that is contained in natural lutetium. In order to mitigate its potential shortcomings, previous works have studied to understand the energy spectrum of the intrinsic radiation of ¹⁷⁶Lu (IRL). However, few studies have focused on the various principal types of photon interactions with matter; in other words, only the full-energy peak according to the photoelectric effect or internal conversion have been considered for understanding the energy spectrum of IRL. Thus, the approach we have used in this study considers other principal types of photon interactions by convoluting each energy spectrum with combinations for generating the spectrum of the intrinsic radiation of ¹⁷⁶Lu. From the results, we confirm that the method provides good agreement with the experiment. A significant contribution of this study is the provision of a new approach to process energy spectra induced by mutually independent radiation interactions as a single spectrum.