We studied a Ce-doped LaAlO3 (LaAP) because of its easy crystal growth facilitated by the large La3+ cations in the matrix. Recent observations of intense blue luminescence by some researchers show that the potential of this material for scintillator applications could not be ruled out. On the other hand, some reports claim that Ce3+ luminescence is completely absent in the LaAP matrix. Therefore, we have decided to study this material in much greater detail using an extended set of correlated experiments to explain the observed discrepancies and underlying phenomena. The luminescence mechanism is proposed and discussed, and the low scintillation efficiency is explained. We concluded that Ce3+ is not luminescent in the LaAP matrix and the occasional observations of luminescence are caused by Al-rich inclusions sometimes created in the material.