Please check out the Offline routing sample. It has a very similar workflow as the online routing. The most significant difference is that the route task is created from a local file, not a URL.
There are 2 ways to create the network dataset for offline use. The recommended approach is to export a mobile map package from ArcGIS Pro with the map's area of interest and all its capabilities. Alternatively, you can construct the map yourself. For instance, create the basemap from a tile cache or tile package, and create the route task from a Network Dataset files (.geodatabase and .tn).
Routing, either online or offline, can be done with a free "Lite" license.
