This dataset contains modelled dispersion of effect refractive indices for three guided modes for a particular lithium niobate nanowaveguide structure. Two of these guided modes show a particularly interesting characteristic of an avoided mode crossing which the work in the associated manuscript is based on. Data is also included for the predicted modulation instability gain for continuous wave solutions in the modelled system. Simulation data for modulation instability are also included showing its impact on the spectrum and formation of trains of solitons from an unstable continuous wave solution. This work also contains predictions made for the solitons that exist in this system. We include data for predicted pulse energy as well as mapping these solitons from their plane of existence onto the linear dispersion of the system. XFROG spectrograms are given for an example soliton solution showing their unusual specro-temporal structure as well as line plots of many solitons temporal and spectral domain separately. Finally we include simulations of soliton propagation in this system.