7Li NMR measurements were performed in the metallic spinel LiV2O4. The temperature dependence of the spin-lattice relaxation rate is documented in the temperature range 100 mK < T < 280 K. A comparison with the spin-glass behavior of Li1xZnxV2O4 for small concentrations of x is given. For low temperatures T < 1 K we observe a maximum for the spin-lattice relaxation rate in LiV2O4. The frequency dependence of this maximum is indicative for a slowing down of spin fluctuations. The NMR results can be explained by a spin-liquid behavior and the opening of a spin gap of the order 1 K. PACS Nos.: 75.20Hr, 75.50Lk, 76.60Es, 76.60-k