Detailed and comparable investigations of the time evolution of the readout erasure of 1D and 2D annular symmetry photonic lattice structures optically induced by nondiffracting Bessel beam technique were performed. The lattices were recorded with the use of cw single mode 532 nm, 17 mW laser beam in photorefractive LiNbO₃:Fe and LiNbO₃:Fe:Cu crystals, the latter having also photochromic properties. While the 1D Bessel-like refractive lattice had micrometric scale modulation in the radial direction, the 2D complex lattices inducted by Bessel standing wave were a combination of annular and planar refractive gratings with ~10 μm period in the radial and half-wavelength standing wave 266 nm period in the axial directions. The study of photochromic properties of LN:Fe:Cu crystal at 532 nm showed 1.6 times increase of absorption coefficient with increase of illuminating intensity from 12.5 to 96.8 mW/cm², which opened a direct way of essential decrease of the erasure of the stored lattices during readout by weaker probe beam at the recording wavelength. Investigations showed that the erasure constants for 1D and 2D lattices in LN:Fe:Cu crystal are larger than in LN:Fe crystal (6150 and 5150 s, and 3080 and 698 s, respectively). The nondestructive refractive lattices recorded by Bessel beam technique will assist the different applications in all optical devices and communication systems and have particular interest for experiments on light localization and spatial soliton formation in structured nonlinear media.