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 J(1)-J(2) model on a square lattice. A sharp single NQR line is observed at the Cu and CI 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 J(1)-J(2) 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(3z(2) - r(2)) orbital (z vertical bar vertical bar c). At 1.5 K, Cu- and Nb-NMR signals disappear above the critical field B-C1 similar or equal to 10.3 T determined from the onset of the magnetization, indicating a field-induced magnetic phase transition at B-C1.