Structural intricacies of the orange-red nitride phosphor system La3-xCexSi6N11 (0 < x <= 3) have been elucidated using a combination of state-of-the art tools, in order to understand the origins of the exceptional optical properties of this important solid-state lighting material. In addition, the optical properties of the end-member (x = 3) compound, Ce3Si6N11, are described for the first time. A combination of synchrotron powder X-ray diffraction and neutron scattering is employed to establish site preferences and the rigid nature of the structure, which is characterized by a high Debye temperature. The high Debye temperature is also corroborated from ab initio electronic structure calculations. Solid-state Si-29 nuclear magnetic resonance, including paramagnetic shifts of Si-29 spectra, are employed in conjunction with low-temperature electron spin resonance studies to probes of the local environments of Ce ions. Detailed wavelength-, time-, and temperature-dependent luminescence properties of the solid solution are presented. Temperature-dependent quantum yield measurements demonstrate the remarkable thermal robustness of luminescence of La2.82Ce0.18Si6Ni11, which shows little sign of thermal quenching, even at temperatures as high as 500 K. This robustness is attributed to the highly rigid lattice. Luminescence decay measurements indicate very short decay times (close to 40 ns). The fast decay is suggested to prevent strong self-quenching of luminescence, allowing even the end-member compound Ce3Si6N11 to display bright luminescence.