The in-plane configurational anisotropy of the frequency and nature of spin-wave modes in two-dimensional artificial Ni₈₀Fe₂₀ nanodot lattices arranged in closely packed rectangular, honeycomb and octagonal lattices are demonstrated by time-resolved magneto-optical Kerr effect measurements. The rectangular, honeycomb and octagonal lattices showed dominant two-fold, six-fold and eight-fold variation of frequency superposed with a weak four-fold anisotropy for specific spin-wave modes with the variation of the azimuthal angle of the external bias magnetic field. Micromagnetic simulations reveal that the observed anisotropy is due to the angular variation of the magnetostatic field distribution and the ensuing spin-wave mode profiles, which varies between arrays. The observations are important for selecting building blocks for future magnetic data storage and magnonic crystals for on-chip microwave communication and processing.