We report magnetization, nuclear magnetic resonance (NMR), nuclear quadrupole resonance (NQR), and transmission electron microscopy (TEM) studies on the quasi-two-dimensional spin-gap system (CuCl)LaNb2O7, a possible candidate for the J1-J2 model on a square lattice. A sharp single NQR line is observed at the Cu and Cl sites, indicating that both Cu and Cl atoms occupy a unique site. However, the electric field gradient tensors at the Cu, Cl, and La sites do not have axial symmetry. This is incompatible with the reported crystal structure. Thus the J1-J2 model has to be modified. We propose alternative two-dimensional dimer models based on the NMR, NQR, and TEM results. The value of the hyperfine coupling constant at the Cu sites indicates that the spin density is mainly on the d(3z2-r2) orbital (z parallel c). At 1.5 K, Cu- and Nb-NMR signals disappear above the critical field Bc1 = 10.3 T determined from the onset of the magnetization, indicating a field-induced magnetic phase transition at Bc1.