Is it possible to use stamen toner-lines tiles as a base map in ArcMap? If so, how are they added as a base map?
Several Stamen maps are available through ArcGIS Online, though not the toner-lines tiles.
ArcBruTile can make external tiles usable as a base map in ArcMap, though the toner-lines tiles aren't one of the "supported maps".
In 2013, Kenneth Field wrote a blog post about using external tilesets in ArcGIS online maps, though the interface for uploading datasets has changed and some of the interfaces/options are no longer presented when following the steps.