$^{139}\mathrm{La}$ NQR and zero-field ${\mathrm{\ensuremath{\mu}}}^{+}$SR in antiferromagnetic (AF) ${\mathrm{La}}_{2}$${\mathrm{Cu}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Zn}}_{\mathit{x}}$${\mathrm{O}}_{4}$, for x up to 0.13 and in the temperature range 1.6--350 K, are used to study the effects related to the substitution of magnetic ${\mathrm{Cu}}^{2+}$ S=1/2 with homovalent diamagnetic S=0 ${\mathrm{Zn}}^{2+}$ in ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$. We report measurements both of static magnetic properties, such as N\'eel temperatures ${\mathit{T}}_{\mathit{N}}$, sublattice magnetization and field \ensuremath{\Vert}h\ensuremath{\Vert} at the La nucleus or at the ${\mathrm{\ensuremath{\mu}}}^{+}$ site, as well as of NQR relaxation rates W. These quantities are used to study the effects of Zn doping on the low-energy ${\mathrm{Cu}}^{2+}$ spin excitations. It is found that ${\mathit{T}}_{\mathit{N}}$ decreases with x in a way close to the one expected by diluting quasi-two-dimensional Heisenberg magnets on square lattice, while the sublattice magnetization is slightly affected by Zn doping. Mean-field arguments based on the dilution model for the interplanar interactions allow one to conclude that the in-plane magnetic correlation length is little sensitive to the Zn presence. Up to x\ensuremath{\simeq}0.08 the temperature dependence of the AF field \ensuremath{\Vert}h\ensuremath{\Vert} is close to the one in pure ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$, with a sharp decrease for T\ensuremath{\rightarrow}${\mathit{T}}_{\mathit{N}}^{\mathrm{\ensuremath{-}}}$ indicative of a continuous transition with a small critical exponent \ensuremath{\beta}.For strong doping the low-temperature dependence of \ensuremath{\Vert}h\ensuremath{\Vert} appears to depart from the one in pure ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$. For x\ensuremath{\ge}0.05 both NQR spectra and \ensuremath{\mu}SR reveal the presence of regions where the long-range AF order is suppressed. For temperature above 100 K up to ${\mathit{T}}_{\mathit{N}}$ the $^{139}\mathrm{La}$ relaxation rate W due to the ${\mathrm{Cu}}^{2+}$ spin fluctuations shows only slight corrections with respect to pure ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ which are possibly related to the disorder in the AF interactions or to finite-size effects. A novel and remarkable effect of Zn doping is the appearance in W, for T\ensuremath{\le}100 K, of large and marked maxima, which are x dependent. This phenomenon is attributed to the cooperative freezing of local magnetic moments induced by Zn on Cu orbitals, interacting via the underlying AF matrix. The maxima in W occur when the fluctuation frequencies of the anomalous spins become of the order of the NQR frequency, thus driving the system to a spin-glass state superimposed to the AF matrix.