I’m not very familiar with SpatiaLite, but we do have built in support for both KML and GeoJson in Cesium.
You may be able to create a custom data source to load your SpatiaLite data directly, you can see an example for that here: http://cesiumjs.org/Cesium/Apps/Sandcastle/index.html?src=Custom%20DataSource.html&label=DataSources
Or you can look at the KML and GeoJson examples. That might be easier if you can easily export to one of those formats. I would recommend GeoJson over KML because it’s a little easier for the browser to load.
If you have very large datasets, you will ultimately want to use the new 3D tiles format for optimal performance. You can learn more about that here: https://groups.google.com/d/msg/cesium-dev/tCCooBxpZFU/7hxT_E4pGgAJ