A novel laterally overmodulated (LOM) structure of lithium niobate photonic crystals (PCs) is presented and theoretically analyzed with band diagrams calculated by the plane-wave expansion technique for periodic structures and transmission spectra evaluated by the 2D finite-difference time domain (FDTD) method. The LOM structure is based on a triangular lattice of air holes drilled in the top surface of a titanium-diffused erbium-doped lithium niobate waveguide Ti:Er:LiNbO3. The LOM operates in a distributed-feedback (DFB)-like regime and its parameters are designed to maximize the spontaneous emission rate at 1.55 µm. The first experiment shows an optical amplification close to 9 dB at 1.55 µm.