I do not have the common attributes to do a regular dissolve. However I can see which lines are separate from another. Either QGIS or ArcGIS is fine.
In arcgis there a tool in the editor toolbar that let you combine the selected feature (you can even choose one feature to keep the attribute from) see : http://desktop.arcgis.com/fr/arcmap/10.3/manage-data/creating-new-features/merging-features-in-the-same-layer.htm
In Qgis there is also a "merge selected feature" that work in the exact same way (you'll find it in the advanced digitizing toolbar).
If you dont have too many lines nor to many merge you can manually select your lines then use the merge tool from your favorite software