Engineered domain structures play an essential role in nonlinear optics for quasi-phase-matched parametric processes. Pyroelectric field-assisted domain inversion with focused femtosecond laser pulses is a promising approach to create arbitrary two-dimensional nonlinear photonic structures in a large volume without externally applied electrical fields. We fabricate lattices of ferroelectric domains by patterning lithium niobate crystals with femtosecond laser pulses and then heating them to elevated temperatures. After cooling to room temperature, domains form below and above the laser-induced seeds. We investigate the effect of temperature and seed spacing on the number and size of inverted domains. In a temperature range of 220 °C-300 °C all domains are inverted in a two-dimensional lattice with periods of 15 µm × 6.3 µm. Smaller lattice periods result in a smaller fraction of inverted domains. Measurements with conducting, nonconducting, and short-circuited crystal surfaces reveal the influence of surface charges during the domain formation process. From the obtained domain widths and spacings, we calculate the effective nonlinear coefficient of quasi-phase-matched second-harmonic generation in two-dimensional nonlinear photonic structures.