We report an electro-optically tunable photonic crystal linear cavity etched on a 200 nm lithium niobate waveguide ridge. The photonic crystal cavity and the ridge are both fabricated on a 1 μm thin film of lithium niobate obtained by smart-cut technology. The photonic crystal, of area 4x0.8 μm2, has been engineered to work in a slow light configuration so that the electro-optic effect is 20 times more important than in bulk material.