We theoretically propose a hybrid lithium niobate (LN) thin-film waveguide that consists of an amorphous silicon stripe and etch-free z-cut LN for highly efficient wavelength conversion, circumventing the challenging etching on LN material. Profiting from the spatial symmetry breaking of the waveguide, the asymmetric hybrid modes can spontaneously achieve phase matching with small modal area and large spatial mode overlap, enabling enhanced second harmonic generation with a normalized conversion efficiency over $3900\%{\mathrm{W}}^{-1}·{\mathrm{cm}}^{-2}$ (0.5-mm-long propagation distance). The choice of integrating silicon with LN alleviates the fabrication challenge, making the platform potentially compatible with silicon photonics.