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LaNiGa₂ is a layered centrosymmetric superconductor with an orthorhombic crystal structure. ??SR experiments have observed spontaneous magnetic fields at the onset of superconducting state, implying time-reversal symmetry breaking and suggesting the possibility of triplet pairing. We report on NQR measurements performed on ¹³⁹La down to dilution fridge temperatures showing a large shift to the spectrum in the superconducting state. We also report on continued normal state NMR measurements on ⁶⁹Ga determining the anisotropy of the electric field gradient at the two 69Ga sites. These measurements are shown to be consistent with band structure calculations.