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Lithium niobate (LN) has been widely used for second-harmonic generation (SHG) from bulk crystals. Recent studies have reported improved SHG efficiency in LN micro-ring resonators and hybrid waveguiding structures, as well as in LN nanostructures supporting anapole modes and plasmon-assisted dipole resonances. Here we numerically demonstrate that high$Q$-factor resonances associated with symmetry-protected bound states in the continuum can lead to highly efficient frequency doubling in LN metasurfaces. Simulations show that the radiative$Q$-factor and on-resonance field enhancement factor observed in the metasurface are closely dependent on the asymmetric parameter$\mathrm{\alpha <\#comment/>}$of the system. Furthermore, high$Q$-factor resonances boost the SH conversion process in the LN nanostructures. In particular, for a LN metasurface with a$Q$-factor of$\sim <\#comment/>8\times <\#comment/>{10}^4$, a 0.49% peak SH conversion efficiency is achieved at a pump intensity of$3.3{\mathrm{k}\mathrm{W}/\mathrm{c}\mathrm{m}}^2$. This suggests that such high$Q$-factor LN metasurfaces may be good candidates for practical blue–ultraviolet light sources. Our work provides insight into the possible implementation of metadevices based on nanoengineering of conventional nonlinear crystals.