In this paper, the size- and shape-dependent spectral characteristics of plasmonic nanostructures based on the Thue-Morse (ThMo) sequence are investigated in theory and experiment. We designed, fabricated, and characterized nine different Au nanopillars (NPs) lattices to evaluate their use as nanosensors based on localized surface plasmon resonances (LSPR). The extinction spectra and the bulk refractive index sensitivity (m) are compared to three selected shapes of the NPs (square, circular, and triangular) with different minimum interparticle distance. The maximum m of 275 nm/RIU is obtained for a ThMo pattern with square NPs. Finally, a detection limit of 260 pM (62 pg/ml) of Thiram pesticide has been achieved using an LSPR nanosensor based on an optimized ThMo pattern with triangular NPs employing a phase-sensitive setup to increase the figure-of-merit (FOM) of the sensor.