Cu-63 NQR and AFNMR, and Li-7 NMR spin-lattice relaxation measurements are used to study the spin dynamics in the paramagnetic (PA) and in the antiferromagnetic (AF) phase and the effects associated with the creation of holes upon lithium doping. The relaxation rates W indicate that the Cu2+ spin dynamics is almost unaffected by Li doping for T >> T(N) and that it is possibly controlled by valence fluctuations. Close to T(N) a crossover to an XY or to an Ising spin system drives the transition to the ordered state. The Li doping modifies in a dramatic way the spin fluctuations in the AF phase, by increasing the relaxation rates by orders of magnitude and inducing temperature behaviour quite different from that in CuO. These effects are related to the fluctuations in the local Cu2+ spin configuration due to the diffusional motion of the extra holes in the electronic bands. A satisfactory explanation of the temperature and frequency dependences of Li relaxation rates is given in terms of a correlation time tau(h) for the hole motion controlled by an energy gap E(x) and quantitative information on tau(h) and E(x) are thus derived.