We report a Li7 nuclear magnetic resonance (NMR) study of a frustrated three-dimensional spin-12 antiferromagnet Li2CuW2O8 and also explore the effect of nonmagnetic dilution. The magnetic long-range ordering in the parent compound at TN≃3.9K was detected from the drastic line broadening and a peak in the spin-lattice relaxation rate (1/T1). The NMR spectrum above TN broadens systematically and its full width at half maximum (FWHM) tracks the static spin susceptibility. From the analysis of FWHM vs static susceptibility, the coupling between the Li nuclei and Cu2+ ions was found to be purely dipolar in nature. The magnitude of the maximum exchange coupling constant is Jmax/kB≃13K. NMR spectra below TN broaden abruptly and transform into a double-horn pattern reflecting the commensurate nature of the spin structure in the ordered state. Below TN, 1/T1 follows a T5 behavior. The frustrated nature of the compound is confirmed by persistent magnetic correlations at high temperatures well above TN. The dilution of the spin lattice with nonmagnetic Zn atoms has dramatic influence on TN that decreases exponentially similar to quasi-one-dimensional antiferromagnets, even though Li2CuW2O8 has only a weak one-dimensional anisotropy. Heat capacity of doped samples follows power law (Cp T$\alpha$) below TN and the exponent ($\alpha$) decreases from 3 in the parent compound to 1 in the 25% doped sample.