We demonstrated lasing in localized optical resonances of deterministic aperiodic structures with pseudo-random morphologies. The localized lasing modes in the Rudin-Shapiro arrays of air nanoholes in GaAs membranes occur at reproducible spatial locations and their frequencies are only slightly affected by the structural fluctuations in different samples. Numerical study on the resonances of the passive systems and optical imaging of lasing modes enabled us to interpret the observed lasing behavior in terms of distinctive localized resonances in the two-dimensional Rudin- Shapiro structures. The deterministic aperiodic media with controllable structural and optical properties provide a novel platform, alternative to random lasers and different from photonic crystals lasers, for the engineering of multi-frequency coherent light sources suitable for technological integration.